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Simplifying 0x = (x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7)(x + 8)(x + 9)(x + 10)(x + 11)(x + 12) * x Anything times zero is zero. 0x = (x + 1)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7)(x + 8)(x + 9)(x + 10)(x + 11)(x + 12) * x Reorder the terms: 0 = (1 + x)(x + 2)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7)(x + 8)(x + 9)(x + 10)(x + 11)(x + 12) * x Reorder the terms: 0 = (1 + x)(2 + x)(x + 3)(x + 4)(x + 5)(x + 6)(x + 7)(x + 8)(x + 9)(x + 10)(x + 11)(x + 12) * x Reorder the terms: 0 = (1 + x)(2 + x)(3 + x)(x + 4)(x + 5)(x + 6)(x + 7)(x + 8)(x + 9)(x + 10)(x + 11)(x + 12) * x Reorder the terms: 0 = (1 + x)(2 + x)(3 + x)(4 + x)(x + 5)(x + 6)(x + 7)(x + 8)(x + 9)(x + 10)(x + 11)(x + 12) * x Reorder the terms: 0 = (1 + x)(2 + x)(3 + x)(4 + x)(5 + x)(x + 6)(x + 7)(x + 8)(x + 9)(x + 10)(x + 11)(x + 12) * x Reorder the terms: 0 = (1 + x)(2 + x)(3 + x)(4 + x)(5 + x)(6 + x)(x + 7)(x + 8)(x + 9)(x + 10)(x + 11)(x + 12) * x Reorder the terms: 0 = (1 + x)(2 + x)(3 + x)(4 + x)(5 + x)(6 + x)(7 + x)(x + 8)(x + 9)(x + 10)(x + 11)(x + 12) * x Reorder the terms: 0 = (1 + x)(2 + x)(3 + x)(4 + x)(5 + x)(6 + x)(7 + x)(8 + x)(x + 9)(x + 10)(x + 11)(x + 12) * x Reorder the terms: 0 = (1 + x)(2 + x)(3 + x)(4 + x)(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(x + 10)(x + 11)(x + 12) * x Reorder the terms: 0 = (1 + x)(2 + x)(3 + x)(4 + x)(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(x + 11)(x + 12) * x Reorder the terms: 0 = (1 + x)(2 + x)(3 + x)(4 + x)(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(x + 12) * x Reorder the terms: 0 = (1 + x)(2 + x)(3 + x)(4 + x)(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) * x Reorder the terms for easier multiplication: 0 = x(1 + x)(2 + x)(3 + x)(4 + x)(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Multiply (1 + x) * (2 + x) 0 = x(1(2 + x) + x(2 + x))(3 + x)(4 + x)(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x((2 * 1 + x * 1) + x(2 + x))(3 + x)(4 + x)(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x((2 + 1x) + x(2 + x))(3 + x)(4 + x)(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(2 + 1x + (2 * x + x * x))(3 + x)(4 + x)(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(2 + 1x + (2x + x2))(3 + x)(4 + x)(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 1x + 2x = 3x 0 = x(2 + 3x + x2)(3 + x)(4 + x)(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Multiply (2 + 3x + x2) * (3 + x) 0 = x(2(3 + x) + 3x * (3 + x) + x2(3 + x))(4 + x)(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x((3 * 2 + x * 2) + 3x * (3 + x) + x2(3 + x))(4 + x)(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x((6 + 2x) + 3x * (3 + x) + x2(3 + x))(4 + x)(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(6 + 2x + (3 * 3x + x * 3x) + x2(3 + x))(4 + x)(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(6 + 2x + (9x + 3x2) + x2(3 + x))(4 + x)(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(6 + 2x + 9x + 3x2 + (3 * x2 + x * x2))(4 + x)(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(6 + 2x + 9x + 3x2 + (3x2 + x3))(4 + x)(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 2x + 9x = 11x 0 = x(6 + 11x + 3x2 + 3x2 + x3)(4 + x)(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 3x2 + 3x2 = 6x2 0 = x(6 + 11x + 6x2 + x3)(4 + x)(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Multiply (6 + 11x + 6x2 + x3) * (4 + x) 0 = x(6(4 + x) + 11x * (4 + x) + 6x2 * (4 + x) + x3(4 + x))(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x((4 * 6 + x * 6) + 11x * (4 + x) + 6x2 * (4 + x) + x3(4 + x))(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x((24 + 6x) + 11x * (4 + x) + 6x2 * (4 + x) + x3(4 + x))(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(24 + 6x + (4 * 11x + x * 11x) + 6x2 * (4 + x) + x3(4 + x))(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(24 + 6x + (44x + 11x2) + 6x2 * (4 + x) + x3(4 + x))(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(24 + 6x + 44x + 11x2 + (4 * 6x2 + x * 6x2) + x3(4 + x))(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(24 + 6x + 44x + 11x2 + (24x2 + 6x3) + x3(4 + x))(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(24 + 6x + 44x + 11x2 + 24x2 + 6x3 + (4 * x3 + x * x3))(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(24 + 6x + 44x + 11x2 + 24x2 + 6x3 + (4x3 + x4))(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 6x + 44x = 50x 0 = x(24 + 50x + 11x2 + 24x2 + 6x3 + 4x3 + x4)(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 11x2 + 24x2 = 35x2 0 = x(24 + 50x + 35x2 + 6x3 + 4x3 + x4)(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 6x3 + 4x3 = 10x3 0 = x(24 + 50x + 35x2 + 10x3 + x4)(5 + x)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Multiply (24 + 50x + 35x2 + 10x3 + x4) * (5 + x) 0 = x(24(5 + x) + 50x * (5 + x) + 35x2 * (5 + x) + 10x3 * (5 + x) + x4(5 + x))(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x((5 * 24 + x * 24) + 50x * (5 + x) + 35x2 * (5 + x) + 10x3 * (5 + x) + x4(5 + x))(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x((120 + 24x) + 50x * (5 + x) + 35x2 * (5 + x) + 10x3 * (5 + x) + x4(5 + x))(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(120 + 24x + (5 * 50x + x * 50x) + 35x2 * (5 + x) + 10x3 * (5 + x) + x4(5 + x))(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(120 + 24x + (250x + 50x2) + 35x2 * (5 + x) + 10x3 * (5 + x) + x4(5 + x))(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(120 + 24x + 250x + 50x2 + (5 * 35x2 + x * 35x2) + 10x3 * (5 + x) + x4(5 + x))(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(120 + 24x + 250x + 50x2 + (175x2 + 35x3) + 10x3 * (5 + x) + x4(5 + x))(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(120 + 24x + 250x + 50x2 + 175x2 + 35x3 + (5 * 10x3 + x * 10x3) + x4(5 + x))(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(120 + 24x + 250x + 50x2 + 175x2 + 35x3 + (50x3 + 10x4) + x4(5 + x))(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(120 + 24x + 250x + 50x2 + 175x2 + 35x3 + 50x3 + 10x4 + (5 * x4 + x * x4))(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(120 + 24x + 250x + 50x2 + 175x2 + 35x3 + 50x3 + 10x4 + (5x4 + x5))(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 24x + 250x = 274x 0 = x(120 + 274x + 50x2 + 175x2 + 35x3 + 50x3 + 10x4 + 5x4 + x5)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 50x2 + 175x2 = 225x2 0 = x(120 + 274x + 225x2 + 35x3 + 50x3 + 10x4 + 5x4 + x5)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 35x3 + 50x3 = 85x3 0 = x(120 + 274x + 225x2 + 85x3 + 10x4 + 5x4 + x5)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 10x4 + 5x4 = 15x4 0 = x(120 + 274x + 225x2 + 85x3 + 15x4 + x5)(6 + x)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Multiply (120 + 274x + 225x2 + 85x3 + 15x4 + x5) * (6 + x) 0 = x(120(6 + x) + 274x * (6 + x) + 225x2 * (6 + x) + 85x3 * (6 + x) + 15x4 * (6 + x) + x5(6 + x))(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x((6 * 120 + x * 120) + 274x * (6 + x) + 225x2 * (6 + x) + 85x3 * (6 + x) + 15x4 * (6 + x) + x5(6 + x))(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x((720 + 120x) + 274x * (6 + x) + 225x2 * (6 + x) + 85x3 * (6 + x) + 15x4 * (6 + x) + x5(6 + x))(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(720 + 120x + (6 * 274x + x * 274x) + 225x2 * (6 + x) + 85x3 * (6 + x) + 15x4 * (6 + x) + x5(6 + x))(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(720 + 120x + (1644x + 274x2) + 225x2 * (6 + x) + 85x3 * (6 + x) + 15x4 * (6 + x) + x5(6 + x))(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(720 + 120x + 1644x + 274x2 + (6 * 225x2 + x * 225x2) + 85x3 * (6 + x) + 15x4 * (6 + x) + x5(6 + x))(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(720 + 120x + 1644x + 274x2 + (1350x2 + 225x3) + 85x3 * (6 + x) + 15x4 * (6 + x) + x5(6 + x))(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(720 + 120x + 1644x + 274x2 + 1350x2 + 225x3 + (6 * 85x3 + x * 85x3) + 15x4 * (6 + x) + x5(6 + x))(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(720 + 120x + 1644x + 274x2 + 1350x2 + 225x3 + (510x3 + 85x4) + 15x4 * (6 + x) + x5(6 + x))(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(720 + 120x + 1644x + 274x2 + 1350x2 + 225x3 + 510x3 + 85x4 + (6 * 15x4 + x * 15x4) + x5(6 + x))(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(720 + 120x + 1644x + 274x2 + 1350x2 + 225x3 + 510x3 + 85x4 + (90x4 + 15x5) + x5(6 + x))(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(720 + 120x + 1644x + 274x2 + 1350x2 + 225x3 + 510x3 + 85x4 + 90x4 + 15x5 + (6 * x5 + x * x5))(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(720 + 120x + 1644x + 274x2 + 1350x2 + 225x3 + 510x3 + 85x4 + 90x4 + 15x5 + (6x5 + x6))(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 120x + 1644x = 1764x 0 = x(720 + 1764x + 274x2 + 1350x2 + 225x3 + 510x3 + 85x4 + 90x4 + 15x5 + 6x5 + x6)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 274x2 + 1350x2 = 1624x2 0 = x(720 + 1764x + 1624x2 + 225x3 + 510x3 + 85x4 + 90x4 + 15x5 + 6x5 + x6)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 225x3 + 510x3 = 735x3 0 = x(720 + 1764x + 1624x2 + 735x3 + 85x4 + 90x4 + 15x5 + 6x5 + x6)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 85x4 + 90x4 = 175x4 0 = x(720 + 1764x + 1624x2 + 735x3 + 175x4 + 15x5 + 6x5 + x6)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 15x5 + 6x5 = 21x5 0 = x(720 + 1764x + 1624x2 + 735x3 + 175x4 + 21x5 + x6)(7 + x)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Multiply (720 + 1764x + 1624x2 + 735x3 + 175x4 + 21x5 + x6) * (7 + x) 0 = x(720(7 + x) + 1764x * (7 + x) + 1624x2 * (7 + x) + 735x3 * (7 + x) + 175x4 * (7 + x) + 21x5 * (7 + x) + x6(7 + x))(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x((7 * 720 + x * 720) + 1764x * (7 + x) + 1624x2 * (7 + x) + 735x3 * (7 + x) + 175x4 * (7 + x) + 21x5 * (7 + x) + x6(7 + x))(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x((5040 + 720x) + 1764x * (7 + x) + 1624x2 * (7 + x) + 735x3 * (7 + x) + 175x4 * (7 + x) + 21x5 * (7 + x) + x6(7 + x))(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(5040 + 720x + (7 * 1764x + x * 1764x) + 1624x2 * (7 + x) + 735x3 * (7 + x) + 175x4 * (7 + x) + 21x5 * (7 + x) + x6(7 + x))(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(5040 + 720x + (12348x + 1764x2) + 1624x2 * (7 + x) + 735x3 * (7 + x) + 175x4 * (7 + x) + 21x5 * (7 + x) + x6(7 + x))(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(5040 + 720x + 12348x + 1764x2 + (7 * 1624x2 + x * 1624x2) + 735x3 * (7 + x) + 175x4 * (7 + x) + 21x5 * (7 + x) + x6(7 + x))(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(5040 + 720x + 12348x + 1764x2 + (11368x2 + 1624x3) + 735x3 * (7 + x) + 175x4 * (7 + x) + 21x5 * (7 + x) + x6(7 + x))(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(5040 + 720x + 12348x + 1764x2 + 11368x2 + 1624x3 + (7 * 735x3 + x * 735x3) + 175x4 * (7 + x) + 21x5 * (7 + x) + x6(7 + x))(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(5040 + 720x + 12348x + 1764x2 + 11368x2 + 1624x3 + (5145x3 + 735x4) + 175x4 * (7 + x) + 21x5 * (7 + x) + x6(7 + x))(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(5040 + 720x + 12348x + 1764x2 + 11368x2 + 1624x3 + 5145x3 + 735x4 + (7 * 175x4 + x * 175x4) + 21x5 * (7 + x) + x6(7 + x))(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(5040 + 720x + 12348x + 1764x2 + 11368x2 + 1624x3 + 5145x3 + 735x4 + (1225x4 + 175x5) + 21x5 * (7 + x) + x6(7 + x))(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(5040 + 720x + 12348x + 1764x2 + 11368x2 + 1624x3 + 5145x3 + 735x4 + 1225x4 + 175x5 + (7 * 21x5 + x * 21x5) + x6(7 + x))(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(5040 + 720x + 12348x + 1764x2 + 11368x2 + 1624x3 + 5145x3 + 735x4 + 1225x4 + 175x5 + (147x5 + 21x6) + x6(7 + x))(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(5040 + 720x + 12348x + 1764x2 + 11368x2 + 1624x3 + 5145x3 + 735x4 + 1225x4 + 175x5 + 147x5 + 21x6 + (7 * x6 + x * x6))(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(5040 + 720x + 12348x + 1764x2 + 11368x2 + 1624x3 + 5145x3 + 735x4 + 1225x4 + 175x5 + 147x5 + 21x6 + (7x6 + x7))(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 720x + 12348x = 13068x 0 = x(5040 + 13068x + 1764x2 + 11368x2 + 1624x3 + 5145x3 + 735x4 + 1225x4 + 175x5 + 147x5 + 21x6 + 7x6 + x7)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 1764x2 + 11368x2 = 13132x2 0 = x(5040 + 13068x + 13132x2 + 1624x3 + 5145x3 + 735x4 + 1225x4 + 175x5 + 147x5 + 21x6 + 7x6 + x7)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 1624x3 + 5145x3 = 6769x3 0 = x(5040 + 13068x + 13132x2 + 6769x3 + 735x4 + 1225x4 + 175x5 + 147x5 + 21x6 + 7x6 + x7)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 735x4 + 1225x4 = 1960x4 0 = x(5040 + 13068x + 13132x2 + 6769x3 + 1960x4 + 175x5 + 147x5 + 21x6 + 7x6 + x7)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 175x5 + 147x5 = 322x5 0 = x(5040 + 13068x + 13132x2 + 6769x3 + 1960x4 + 322x5 + 21x6 + 7x6 + x7)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 21x6 + 7x6 = 28x6 0 = x(5040 + 13068x + 13132x2 + 6769x3 + 1960x4 + 322x5 + 28x6 + x7)(8 + x)(9 + x)(10 + x)(11 + x)(12 + x) Multiply (5040 + 13068x + 13132x2 + 6769x3 + 1960x4 + 322x5 + 28x6 + x7) * (8 + x) 0 = x(5040(8 + x) + 13068x * (8 + x) + 13132x2 * (8 + x) + 6769x3 * (8 + x) + 1960x4 * (8 + x) + 322x5 * (8 + x) + 28x6 * (8 + x) + x7(8 + x))(9 + x)(10 + x)(11 + x)(12 + x) 0 = x((8 * 5040 + x * 5040) + 13068x * (8 + x) + 13132x2 * (8 + x) + 6769x3 * (8 + x) + 1960x4 * (8 + x) + 322x5 * (8 + x) + 28x6 * (8 + x) + x7(8 + x))(9 + x)(10 + x)(11 + x)(12 + x) 0 = x((40320 + 5040x) + 13068x * (8 + x) + 13132x2 * (8 + x) + 6769x3 * (8 + x) + 1960x4 * (8 + x) + 322x5 * (8 + x) + 28x6 * (8 + x) + x7(8 + x))(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(40320 + 5040x + (8 * 13068x + x * 13068x) + 13132x2 * (8 + x) + 6769x3 * (8 + x) + 1960x4 * (8 + x) + 322x5 * (8 + x) + 28x6 * (8 + x) + x7(8 + x))(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(40320 + 5040x + (104544x + 13068x2) + 13132x2 * (8 + x) + 6769x3 * (8 + x) + 1960x4 * (8 + x) + 322x5 * (8 + x) + 28x6 * (8 + x) + x7(8 + x))(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(40320 + 5040x + 104544x + 13068x2 + (8 * 13132x2 + x * 13132x2) + 6769x3 * (8 + x) + 1960x4 * (8 + x) + 322x5 * (8 + x) + 28x6 * (8 + x) + x7(8 + x))(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(40320 + 5040x + 104544x + 13068x2 + (105056x2 + 13132x3) + 6769x3 * (8 + x) + 1960x4 * (8 + x) + 322x5 * (8 + x) + 28x6 * (8 + x) + x7(8 + x))(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(40320 + 5040x + 104544x + 13068x2 + 105056x2 + 13132x3 + (8 * 6769x3 + x * 6769x3) + 1960x4 * (8 + x) + 322x5 * (8 + x) + 28x6 * (8 + x) + x7(8 + x))(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(40320 + 5040x + 104544x + 13068x2 + 105056x2 + 13132x3 + (54152x3 + 6769x4) + 1960x4 * (8 + x) + 322x5 * (8 + x) + 28x6 * (8 + x) + x7(8 + x))(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(40320 + 5040x + 104544x + 13068x2 + 105056x2 + 13132x3 + 54152x3 + 6769x4 + (8 * 1960x4 + x * 1960x4) + 322x5 * (8 + x) + 28x6 * (8 + x) + x7(8 + x))(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(40320 + 5040x + 104544x + 13068x2 + 105056x2 + 13132x3 + 54152x3 + 6769x4 + (15680x4 + 1960x5) + 322x5 * (8 + x) + 28x6 * (8 + x) + x7(8 + x))(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(40320 + 5040x + 104544x + 13068x2 + 105056x2 + 13132x3 + 54152x3 + 6769x4 + 15680x4 + 1960x5 + (8 * 322x5 + x * 322x5) + 28x6 * (8 + x) + x7(8 + x))(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(40320 + 5040x + 104544x + 13068x2 + 105056x2 + 13132x3 + 54152x3 + 6769x4 + 15680x4 + 1960x5 + (2576x5 + 322x6) + 28x6 * (8 + x) + x7(8 + x))(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(40320 + 5040x + 104544x + 13068x2 + 105056x2 + 13132x3 + 54152x3 + 6769x4 + 15680x4 + 1960x5 + 2576x5 + 322x6 + (8 * 28x6 + x * 28x6) + x7(8 + x))(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(40320 + 5040x + 104544x + 13068x2 + 105056x2 + 13132x3 + 54152x3 + 6769x4 + 15680x4 + 1960x5 + 2576x5 + 322x6 + (224x6 + 28x7) + x7(8 + x))(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(40320 + 5040x + 104544x + 13068x2 + 105056x2 + 13132x3 + 54152x3 + 6769x4 + 15680x4 + 1960x5 + 2576x5 + 322x6 + 224x6 + 28x7 + (8 * x7 + x * x7))(9 + x)(10 + x)(11 + x)(12 + x) 0 = x(40320 + 5040x + 104544x + 13068x2 + 105056x2 + 13132x3 + 54152x3 + 6769x4 + 15680x4 + 1960x5 + 2576x5 + 322x6 + 224x6 + 28x7 + (8x7 + x8))(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 5040x + 104544x = 109584x 0 = x(40320 + 109584x + 13068x2 + 105056x2 + 13132x3 + 54152x3 + 6769x4 + 15680x4 + 1960x5 + 2576x5 + 322x6 + 224x6 + 28x7 + 8x7 + x8)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 13068x2 + 105056x2 = 118124x2 0 = x(40320 + 109584x + 118124x2 + 13132x3 + 54152x3 + 6769x4 + 15680x4 + 1960x5 + 2576x5 + 322x6 + 224x6 + 28x7 + 8x7 + x8)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 13132x3 + 54152x3 = 67284x3 0 = x(40320 + 109584x + 118124x2 + 67284x3 + 6769x4 + 15680x4 + 1960x5 + 2576x5 + 322x6 + 224x6 + 28x7 + 8x7 + x8)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 6769x4 + 15680x4 = 22449x4 0 = x(40320 + 109584x + 118124x2 + 67284x3 + 22449x4 + 1960x5 + 2576x5 + 322x6 + 224x6 + 28x7 + 8x7 + x8)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 1960x5 + 2576x5 = 4536x5 0 = x(40320 + 109584x + 118124x2 + 67284x3 + 22449x4 + 4536x5 + 322x6 + 224x6 + 28x7 + 8x7 + x8)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 322x6 + 224x6 = 546x6 0 = x(40320 + 109584x + 118124x2 + 67284x3 + 22449x4 + 4536x5 + 546x6 + 28x7 + 8x7 + x8)(9 + x)(10 + x)(11 + x)(12 + x) Combine like terms: 28x7 + 8x7 = 36x7 0 = x(40320 + 109584x + 118124x2 + 67284x3 + 22449x4 + 4536x5 + 546x6 + 36x7 + x8)(9 + x)(10 + x)(11 + x)(12 + x) Multiply (40320 + 109584x + 118124x2 + 67284x3 + 22449x4 + 4536x5 + 546x6 + 36x7 + x8) * (9 + x) 0 = x(40320(9 + x) + 109584x * (9 + x) + 118124x2 * (9 + x) + 67284x3 * (9 + x) + 22449x4 * (9 + x) + 4536x5 * (9 + x) + 546x6 * (9 + x) + 36x7 * (9 + x) + x8(9 + x))(10 + x)(11 + x)(12 + x) 0 = x((9 * 40320 + x * 40320) + 109584x * (9 + x) + 118124x2 * (9 + x) + 67284x3 * (9 + x) + 22449x4 * (9 + x) + 4536x5 * (9 + x) + 546x6 * (9 + x) + 36x7 * (9 + x) + x8(9 + x))(10 + x)(11 + x)(12 + x) 0 = x((362880 + 40320x) + 109584x * (9 + x) + 118124x2 * (9 + x) + 67284x3 * (9 + x) + 22449x4 * (9 + x) + 4536x5 * (9 + x) + 546x6 * (9 + x) + 36x7 * (9 + x) + x8(9 + x))(10 + x)(11 + x)(12 + x) 0 = x(362880 + 40320x + (9 * 109584x + x * 109584x) + 118124x2 * (9 + x) + 67284x3 * (9 + x) + 22449x4 * (9 + x) + 4536x5 * (9 + x) + 546x6 * (9 + x) + 36x7 * (9 + x) + x8(9 + x))(10 + x)(11 + x)(12 + x) 0 = x(362880 + 40320x + (986256x + 109584x2) + 118124x2 * (9 + x) + 67284x3 * (9 + x) + 22449x4 * (9 + x) + 4536x5 * (9 + x) + 546x6 * (9 + x) + 36x7 * (9 + x) + x8(9 + x))(10 + x)(11 + x)(12 + x) 0 = x(362880 + 40320x + 986256x + 109584x2 + (9 * 118124x2 + x * 118124x2) + 67284x3 * (9 + x) + 22449x4 * (9 + x) + 4536x5 * (9 + x) + 546x6 * (9 + x) + 36x7 * (9 + x) + x8(9 + x))(10 + x)(11 + x)(12 + x) 0 = x(362880 + 40320x + 986256x + 109584x2 + (1063116x2 + 118124x3) + 67284x3 * (9 + x) + 22449x4 * (9 + x) + 4536x5 * (9 + x) + 546x6 * (9 + x) + 36x7 * (9 + x) + x8(9 + x))(10 + x)(11 + x)(12 + x) 0 = x(362880 + 40320x + 986256x + 109584x2 + 1063116x2 + 118124x3 + (9 * 67284x3 + x * 67284x3) + 22449x4 * (9 + x) + 4536x5 * (9 + x) + 546x6 * (9 + x) + 36x7 * (9 + x) + x8(9 + x))(10 + x)(11 + x)(12 + x) 0 = x(362880 + 40320x + 986256x + 109584x2 + 1063116x2 + 118124x3 + (605556x3 + 67284x4) + 22449x4 * (9 + x) + 4536x5 * (9 + x) + 546x6 * (9 + x) + 36x7 * (9 + x) + x8(9 + x))(10 + x)(11 + x)(12 + x) 0 = x(362880 + 40320x + 986256x + 109584x2 + 1063116x2 + 118124x3 + 605556x3 + 67284x4 + (9 * 22449x4 + x * 22449x4) + 4536x5 * (9 + x) + 546x6 * (9 + x) + 36x7 * (9 + x) + x8(9 + x))(10 + x)(11 + x)(12 + x) 0 = x(362880 + 40320x + 986256x + 109584x2 + 1063116x2 + 118124x3 + 605556x3 + 67284x4 + (202041x4 + 22449x5) + 4536x5 * (9 + x) + 546x6 * (9 + x) + 36x7 * (9 + x) + x8(9 + x))(10 + x)(11 + x)(12 + x) 0 = x(362880 + 40320x + 986256x + 109584x2 + 1063116x2 + 118124x3 + 605556x3 + 67284x4 + 202041x4 + 22449x5 + (9 * 4536x5 + x * 4536x5) + 546x6 * (9 + x) + 36x7 * (9 + x) + x8(9 + x))(10 + x)(11 + x)(12 + x) 0 = x(362880 + 40320x + 986256x + 109584x2 + 1063116x2 + 118124x3 + 605556x3 + 67284x4 + 202041x4 + 22449x5 + (40824x5 + 4536x6) + 546x6 * (9 + x) + 36x7 * (9 + x) + x8(9 + x))(10 + x)(11 + x)(12 + x) 0 = x(362880 + 40320x + 986256x + 109584x2 + 1063116x2 + 118124x3 + 605556x3 + 67284x4 + 202041x4 + 22449x5 + 40824x5 + 4536x6 + (9 * 546x6 + x * 546x6) + 36x7 * (9 + x) + x8(9 + x))(10 + x)(11 + x)(12 + x) 0 = x(362880 + 40320x + 986256x + 109584x2 + 1063116x2 + 118124x3 + 605556x3 + 67284x4 + 202041x4 + 22449x5 + 40824x5 + 4536x6 + (4914x6 + 546x7) + 36x7 * (9 + x) + x8(9 + x))(10 + x)(11 + x)(12 + x) 0 = x(362880 + 40320x + 986256x + 109584x2 + 1063116x2 + 118124x3 + 605556x3 + 67284x4 + 202041x4 + 22449x5 + 40824x5 + 4536x6 + 4914x6 + 546x7 + (9 * 36x7 + x * 36x7) + x8(9 + x))(10 + x)(11 + x)(12 + x) 0 = x(362880 + 40320x + 986256x + 109584x2 + 1063116x2 + 118124x3 + 605556x3 + 67284x4 + 202041x4 + 22449x5 + 40824x5 + 4536x6 + 4914x6 + 546x7 + (324x7 + 36x8) + x8(9 + x))(10 + x)(11 + x)(12 + x) 0 = x(362880 + 40320x + 986256x + 109584x2 + 1063116x2 + 118124x3 + 605556x3 + 67284x4 + 202041x4 + 22449x5 + 40824x5 + 4536x6 + 4914x6 + 546x7 + 324x7 + 36x8 + (9 * x8 + x * x8))(10 + x)(11 + x)(12 + x) 0 = x(362880 + 40320x + 986256x + 109584x2 + 1063116x2 + 118124x3 + 605556x3 + 67284x4 + 202041x4 + 22449x5 + 40824x5 + 4536x6 + 4914x6 + 546x7 + 324x7 + 36x8 + (9x8 + x9))(10 + x)(11 + x)(12 + x) Combine like terms: 40320x + 986256x = 1026576x 0 = x(362880 + 1026576x + 109584x2 + 1063116x2 + 118124x3 + 605556x3 + 67284x4 + 202041x4 + 22449x5 + 40824x5 + 4536x6 + 4914x6 + 546x7 + 324x7 + 36x8 + 9x8 + x9)(10 + x)(11 + x)(12 + x) Combine like terms: 109584x2 + 1063116x2 = 1172700x2 0 = x(362880 + 1026576x + 1172700x2 + 118124x3 + 605556x3 + 67284x4 + 202041x4 + 22449x5 + 40824x5 + 4536x6 + 4914x6 + 546x7 + 324x7 + 36x8 + 9x8 + x9)(10 + x)(11 + x)(12 + x) Combine like terms: 118124x3 + 605556x3 = 723680x3 0 = x(362880 + 1026576x + 1172700x2 + 723680x3 + 67284x4 + 202041x4 + 22449x5 + 40824x5 + 4536x6 + 4914x6 + 546x7 + 324x7 + 36x8 + 9x8 + x9)(10 + x)(11 + x)(12 + x) Combine like terms: 67284x4 + 202041x4 = 269325x4 0 = x(362880 + 1026576x + 1172700x2 + 723680x3 + 269325x4 + 22449x5 + 40824x5 + 4536x6 + 4914x6 + 546x7 + 324x7 + 36x8 + 9x8 + x9)(10 + x)(11 + x)(12 + x) Combine like terms: 22449x5 + 40824x5 = 63273x5 0 = x(362880 + 1026576x + 1172700x2 + 723680x3 + 269325x4 + 63273x5 + 4536x6 + 4914x6 + 546x7 + 324x7 + 36x8 + 9x8 + x9)(10 + x)(11 + x)(12 + x) Combine like terms: 4536x6 + 4914x6 = 9450x6 0 = x(362880 + 1026576x + 1172700x2 + 723680x3 + 269325x4 + 63273x5 + 9450x6 + 546x7 + 324x7 + 36x8 + 9x8 + x9)(10 + x)(11 + x)(12 + x) Combine like terms: 546x7 + 324x7 = 870x7 0 = x(362880 + 1026576x + 1172700x2 + 723680x3 + 269325x4 + 63273x5 + 9450x6 + 870x7 + 36x8 + 9x8 + x9)(10 + x)(11 + x)(12 + x) Combine like terms: 36x8 + 9x8 = 45x8 0 = x(362880 + 1026576x + 1172700x2 + 723680x3 + 269325x4 + 63273x5 + 9450x6 + 870x7 + 45x8 + x9)(10 + x)(11 + x)(12 + x) Multiply (362880 + 1026576x + 1172700x2 + 723680x3 + 269325x4 + 63273x5 + 9450x6 + 870x7 + 45x8 + x9) * (10 + x) 0 = x(362880(10 + x) + 1026576x * (10 + x) + 1172700x2 * (10 + x) + 723680x3 * (10 + x) + 269325x4 * (10 + x) + 63273x5 * (10 + x) + 9450x6 * (10 + x) + 870x7 * (10 + x) + 45x8 * (10 + x) + x9(10 + x))(11 + x)(12 + x) 0 = x((10 * 362880 + x * 362880) + 1026576x * (10 + x) + 1172700x2 * (10 + x) + 723680x3 * (10 + x) + 269325x4 * (10 + x) + 63273x5 * (10 + x) + 9450x6 * (10 + x) + 870x7 * (10 + x) + 45x8 * (10 + x) + x9(10 + x))(11 + x)(12 + x) 0 = x((3628800 + 362880x) + 1026576x * (10 + x) + 1172700x2 * (10 + x) + 723680x3 * (10 + x) + 269325x4 * (10 + x) + 63273x5 * (10 + x) + 9450x6 * (10 + x) + 870x7 * (10 + x) + 45x8 * (10 + x) + x9(10 + x))(11 + x)(12 + x) 0 = x(3628800 + 362880x + (10 * 1026576x + x * 1026576x) + 1172700x2 * (10 + x) + 723680x3 * (10 + x) + 269325x4 * (10 + x) + 63273x5 * (10 + x) + 9450x6 * (10 + x) + 870x7 * (10 + x) + 45x8 * (10 + x) + x9(10 + x))(11 + x)(12 + x) 0 = x(3628800 + 362880x + (10265760x + 1026576x2) + 1172700x2 * (10 + x) + 723680x3 * (10 + x) + 269325x4 * (10 + x) + 63273x5 * (10 + x) + 9450x6 * (10 + x) + 870x7 * (10 + x) + 45x8 * (10 + x) + x9(10 + x))(11 + x)(12 + x) 0 = x(3628800 + 362880x + 10265760x + 1026576x2 + (10 * 1172700x2 + x * 1172700x2) + 723680x3 * (10 + x) + 269325x4 * (10 + x) + 63273x5 * (10 + x) + 9450x6 * (10 + x) + 870x7 * (10 + x) + 45x8 * (10 + x) + x9(10 + x))(11 + x)(12 + x) 0 = x(3628800 + 362880x + 10265760x + 1026576x2 + (11727000x2 + 1172700x3) + 723680x3 * (10 + x) + 269325x4 * (10 + x) + 63273x5 * (10 + x) + 9450x6 * (10 + x) + 870x7 * (10 + x) + 45x8 * (10 + x) + x9(10 + x))(11 + x)(12 + x) 0 = x(3628800 + 362880x + 10265760x + 1026576x2 + 11727000x2 + 1172700x3 + (10 * 723680x3 + x * 723680x3) + 269325x4 * (10 + x) + 63273x5 * (10 + x) + 9450x6 * (10 + x) + 870x7 * (10 + x) + 45x8 * (10 + x) + x9(10 + x))(11 + x)(12 + x) 0 = x(3628800 + 362880x + 10265760x + 1026576x2 + 11727000x2 + 1172700x3 + (7236800x3 + 723680x4) + 269325x4 * (10 + x) + 63273x5 * (10 + x) + 9450x6 * (10 + x) + 870x7 * (10 + x) + 45x8 * (10 + x) + x9(10 + x))(11 + x)(12 + x) 0 = x(3628800 + 362880x + 10265760x + 1026576x2 + 11727000x2 + 1172700x3 + 7236800x3 + 723680x4 + (10 * 269325x4 + x * 269325x4) + 63273x5 * (10 + x) + 9450x6 * (10 + x) + 870x7 * (10 + x) + 45x8 * (10 + x) + x9(10 + x))(11 + x)(12 + x) 0 = x(3628800 + 362880x + 10265760x + 1026576x2 + 11727000x2 + 1172700x3 + 7236800x3 + 723680x4 + (2693250x4 + 269325x5) + 63273x5 * (10 + x) + 9450x6 * (10 + x) + 870x7 * (10 + x) + 45x8 * (10 + x) + x9(10 + x))(11 + x)(12 + x) 0 = x(3628800 + 362880x + 10265760x + 1026576x2 + 11727000x2 + 1172700x3 + 7236800x3 + 723680x4 + 2693250x4 + 269325x5 + (10 * 63273x5 + x * 63273x5) + 9450x6 * (10 + x) + 870x7 * (10 + x) + 45x8 * (10 + x) + x9(10 + x))(11 + x)(12 + x) 0 = x(3628800 + 362880x + 10265760x + 1026576x2 + 11727000x2 + 1172700x3 + 7236800x3 + 723680x4 + 2693250x4 + 269325x5 + (632730x5 + 63273x6) + 9450x6 * (10 + x) + 870x7 * (10 + x) + 45x8 * (10 + x) + x9(10 + x))(11 + x)(12 + x) 0 = x(3628800 + 362880x + 10265760x + 1026576x2 + 11727000x2 + 1172700x3 + 7236800x3 + 723680x4 + 2693250x4 + 269325x5 + 632730x5 + 63273x6 + (10 * 9450x6 + x * 9450x6) + 870x7 * (10 + x) + 45x8 * (10 + x) + x9(10 + x))(11 + x)(12 + x) 0 = x(3628800 + 362880x + 10265760x + 1026576x2 + 11727000x2 + 1172700x3 + 7236800x3 + 723680x4 + 2693250x4 + 269325x5 + 632730x5 + 63273x6 + (94500x6 + 9450x7) + 870x7 * (10 + x) + 45x8 * (10 + x) + x9(10 + x))(11 + x)(12 + x) 0 = x(3628800 + 362880x + 10265760x + 1026576x2 + 11727000x2 + 1172700x3 + 7236800x3 + 723680x4 + 2693250x4 + 269325x5 + 632730x5 + 63273x6 + 94500x6 + 9450x7 + (10 * 870x7 + x * 870x7) + 45x8 * (10 + x) + x9(10 + x))(11 + x)(12 + x) 0 = x(3628800 + 362880x + 10265760x + 1026576x2 + 11727000x2 + 1172700x3 + 7236800x3 + 723680x4 + 2693250x4 + 269325x5 + 632730x5 + 63273x6 + 94500x6 + 9450x7 + (8700x7 + 870x8) + 45x8 * (10 + x) + x9(10 + x))(11 + x)(12 + x) 0 = x(3628800 + 362880x + 10265760x + 1026576x2 + 11727000x2 + 1172700x3 + 7236800x3 + 723680x4 + 2693250x4 + 269325x5 + 632730x5 + 63273x6 + 94500x6 + 9450x7 + 8700x7 + 870x8 + (10 * 45x8 + x * 45x8) + x9(10 + x))(11 + x)(12 + x) 0 = x(3628800 + 362880x + 10265760x + 1026576x2 + 11727000x2 + 1172700x3 + 7236800x3 + 723680x4 + 2693250x4 + 269325x5 + 632730x5 + 63273x6 + 94500x6 + 9450x7 + 8700x7 + 870x8 + (450x8 + 45x9) + x9(10 + x))(11 + x)(12 + x) 0 = x(3628800 + 362880x + 10265760x + 1026576x2 + 11727000x2 + 1172700x3 + 7236800x3 + 723680x4 + 2693250x4 + 269325x5 + 632730x5 + 63273x6 + 94500x6 + 9450x7 + 8700x7 + 870x8 + 450x8 + 45x9 + (10 * x9 + x * x9))(11 + x)(12 + x) 0 = x(3628800 + 362880x + 10265760x + 1026576x2 + 11727000x2 + 1172700x3 + 7236800x3 + 723680x4 + 2693250x4 + 269325x5 + 632730x5 + 63273x6 + 94500x6 + 9450x7 + 8700x7 + 870x8 + 450x8 + 45x9 + (10x9 + x10))(11 + x)(12 + x) Combine like terms: 362880x + 10265760x = 10628640x 0 = x(3628800 + 10628640x + 1026576x2 + 11727000x2 + 1172700x3 + 7236800x3 + 723680x4 + 2693250x4 + 269325x5 + 632730x5 + 63273x6 + 94500x6 + 9450x7 + 8700x7 + 870x8 + 450x8 + 45x9 + 10x9 + x10)(11 + x)(12 + x) Combine like terms: 1026576x2 + 11727000x2 = 12753576x2 0 = x(3628800 + 10628640x + 12753576x2 + 1172700x3 + 7236800x3 + 723680x4 + 2693250x4 + 269325x5 + 632730x5 + 63273x6 + 94500x6 + 9450x7 + 8700x7 + 870x8 + 450x8 + 45x9 + 10x9 + x10)(11 + x)(12 + x) Combine like terms: 1172700x3 + 7236800x3 = 8409500x3 0 = x(3628800 + 10628640x + 12753576x2 + 8409500x3 + 723680x4 + 2693250x4 + 269325x5 + 632730x5 + 63273x6 + 94500x6 + 9450x7 + 8700x7 + 870x8 + 450x8 + 45x9 + 10x9 + x10)(11 + x)(12 + x) Combine like terms: 723680x4 + 2693250x4 = 3416930x4 0 = x(3628800 + 10628640x + 12753576x2 + 8409500x3 + 3416930x4 + 269325x5 + 632730x5 + 63273x6 + 94500x6 + 9450x7 + 8700x7 + 870x8 + 450x8 + 45x9 + 10x9 + x10)(11 + x)(12 + x) Combine like terms: 269325x5 + 632730x5 = 902055x5 0 = x(3628800 + 10628640x + 12753576x2 + 8409500x3 + 3416930x4 + 902055x5 + 63273x6 + 94500x6 + 9450x7 + 8700x7 + 870x8 + 450x8 + 45x9 + 10x9 + x10)(11 + x)(12 + x) Combine like terms: 63273x6 + 94500x6 = 157773x6 0 = x(3628800 + 10628640x + 12753576x2 + 8409500x3 + 3416930x4 + 902055x5 + 157773x6 + 9450x7 + 8700x7 + 870x8 + 450x8 + 45x9 + 10x9 + x10)(11 + x)(12 + x) Combine like terms: 9450x7 + 8700x7 = 18150x7 0 = x(3628800 + 10628640x + 12753576x2 + 8409500x3 + 3416930x4 + 902055x5 + 157773x6 + 18150x7 + 870x8 + 450x8 + 45x9 + 10x9 + x10)(11 + x)(12 + x) Combine like terms: 870x8 + 450x8 = 1320x8 0 = x(3628800 + 10628640x + 12753576x2 + 8409500x3 + 3416930x4 + 902055x5 + 157773x6 + 18150x7 + 1320x8 + 45x9 + 10x9 + x10)(11 + x)(12 + x) Combine like terms: 45x9 + 10x9 = 55x9 0 = x(3628800 + 10628640x + 12753576x2 + 8409500x3 + 3416930x4 + 902055x5 + 157773x6 + 18150x7 + 1320x8 + 55x9 + x10)(11 + x)(12 + x) Multiply (3628800 + 10628640x + 12753576x2 + 8409500x3 + 3416930x4 + 902055x5 + 157773x6 + 18150x7 + 1320x8 + 55x9 + x10) * (11 + x) 0 = x(3628800(11 + x) + 10628640x * (11 + x) + 12753576x2 * (11 + x) + 8409500x3 * (11 + x) + 3416930x4 * (11 + x) + 902055x5 * (11 + x) + 157773x6 * (11 + x) + 18150x7 * (11 + x) + 1320x8 * (11 + x) + 55x9 * (11 + x) + x10(11 + x))(12 + x) 0 = x((11 * 3628800 + x * 3628800) + 10628640x * (11 + x) + 12753576x2 * (11 + x) + 8409500x3 * (11 + x) + 3416930x4 * (11 + x) + 902055x5 * (11 + x) + 157773x6 * (11 + x) + 18150x7 * (11 + x) + 1320x8 * (11 + x) + 55x9 * (11 + x) + x10(11 + x))(12 + x) 0 = x((39916800 + 3628800x) + 10628640x * (11 + x) + 12753576x2 * (11 + x) + 8409500x3 * (11 + x) + 3416930x4 * (11 + x) + 902055x5 * (11 + x) + 157773x6 * (11 + x) + 18150x7 * (11 + x) + 1320x8 * (11 + x) + 55x9 * (11 + x) + x10(11 + x))(12 + x) 0 = x(39916800 + 3628800x + (11 * 10628640x + x * 10628640x) + 12753576x2 * (11 + x) + 8409500x3 * (11 + x) + 3416930x4 * (11 + x) + 902055x5 * (11 + x) + 157773x6 * (11 + x) + 18150x7 * (11 + x) + 1320x8 * (11 + x) + 55x9 * (11 + x) + x10(11 + x))(12 + x) 0 = x(39916800 + 3628800x + (116915040x + 10628640x2) + 12753576x2 * (11 + x) + 8409500x3 * (11 + x) + 3416930x4 * (11 + x) + 902055x5 * (11 + x) + 157773x6 * (11 + x) + 18150x7 * (11 + x) + 1320x8 * (11 + x) + 55x9 * (11 + x) + x10(11 + x))(12 + x) 0 = x(39916800 + 3628800x + 116915040x + 10628640x2 + (11 * 12753576x2 + x * 12753576x2) + 8409500x3 * (11 + x) + 3416930x4 * (11 + x) + 902055x5 * (11 + x) + 157773x6 * (11 + x) + 18150x7 * (11 + x) + 1320x8 * (11 + x) + 55x9 * (11 + x) + x10(11 + x))(12 + x) 0 = x(39916800 + 3628800x + 116915040x + 10628640x2 + (140289336x2 + 12753576x3) + 8409500x3 * (11 + x) + 3416930x4 * (11 + x) + 902055x5 * (11 + x) + 157773x6 * (11 + x) + 18150x7 * (11 + x) + 1320x8 * (11 + x) + 55x9 * (11 + x) + x10(11 + x))(12 + x) 0 = x(39916800 + 3628800x + 116915040x + 10628640x2 + 140289336x2 + 12753576x3 + (11 * 8409500x3 + x * 8409500x3) + 3416930x4 * (11 + x) + 902055x5 * (11 + x) + 157773x6 * (11 + x) + 18150x7 * (11 + x) + 1320x8 * (11 + x) + 55x9 * (11 + x) + x10(11 + x))(12 + x) 0 = x(39916800 + 3628800x + 116915040x + 10628640x2 + 140289336x2 + 12753576x3 + (92504500x3 + 8409500x4) + 3416930x4 * (11 + x) + 902055x5 * (11 + x) + 157773x6 * (11 + x) + 18150x7 * (11 + x) + 1320x8 * (11 + x) + 55x9 * (11 + x) + x10(11 + x))(12 + x) 0 = x(39916800 + 3628800x + 116915040x + 10628640x2 + 140289336x2 + 12753576x3 + 92504500x3 + 8409500x4 + (11 * 3416930x4 + x * 3416930x4) + 902055x5 * (11 + x) + 157773x6 * (11 + x) + 18150x7 * (11 + x) + 1320x8 * (11 + x) + 55x9 * (11 + x) + x10(11 + x))(12 + x) 0 = x(39916800 + 3628800x + 116915040x + 10628640x2 + 140289336x2 + 12753576x3 + 92504500x3 + 8409500x4 + (37586230x4 + 3416930x5) + 902055x5 * (11 + x) + 157773x6 * (11 + x) + 18150x7 * (11 + x) + 1320x8 * (11 + x) + 55x9 * (11 + x) + x10(11 + x))(12 + x) 0 = x(39916800 + 3628800x + 116915040x + 10628640x2 + 140289336x2 + 12753576x3 + 92504500x3 + 8409500x4 + 37586230x4 + 3416930x5 + (11 * 902055x5 + x * 902055x5) + 157773x6 * (11 + x) + 18150x7 * (11 + x) + 1320x8 * (11 + x) + 55x9 * (11 + x) + x10(11 + x))(12 + x) 0 = x(39916800 + 3628800x + 116915040x + 10628640x2 + 140289336x2 + 12753576x3 + 92504500x3 + 8409500x4 + 37586230x4 + 3416930x5 + (9922605x5 + 902055x6) + 157773x6 * (11 + x) + 18150x7 * (11 + x) + 1320x8 * (11 + x) + 55x9 * (11 + x) + x10(11 + x))(12 + x) 0 = x(39916800 + 3628800x + 116915040x + 10628640x2 + 140289336x2 + 12753576x3 + 92504500x3 + 8409500x4 + 37586230x4 + 3416930x5 + 9922605x5 + 902055x6 + (11 * 157773x6 + x * 157773x6) + 18150x7 * (11 + x) + 1320x8 * (11 + x) + 55x9 * (11 + x) + x10(11 + x))(12 + x) 0 = x(39916800 + 3628800x + 116915040x + 10628640x2 + 140289336x2 + 12753576x3 + 92504500x3 + 8409500x4 + 37586230x4 + 3416930x5 + 9922605x5 + 902055x6 + (1735503x6 + 157773x7) + 18150x7 * (11 + x) + 1320x8 * (11 + x) + 55x9 * (11 + x) + x10(11 + x))(12 + x) 0 = x(39916800 + 3628800x + 116915040x + 10628640x2 + 140289336x2 + 12753576x3 + 92504500x3 + 8409500x4 + 37586230x4 + 3416930x5 + 9922605x5 + 902055x6 + 1735503x6 + 157773x7 + (11 * 18150x7 + x * 18150x7) + 1320x8 * (11 + x) + 55x9 * (11 + x) + x10(11 + x))(12 + x) 0 = x(39916800 + 3628800x + 116915040x + 10628640x2 + 140289336x2 + 12753576x3 + 92504500x3 + 8409500x4 + 37586230x4 + 3416930x5 + 9922605x5 + 902055x6 + 1735503x6 + 157773x7 + (199650x7 + 18150x8) + 1320x8 * (11 + x) + 55x9 * (11 + x) + x10(11 + x))(12 + x) 0 = x(39916800 + 3628800x + 116915040x + 10628640x2 + 140289336x2 + 12753576x3 + 92504500x3 + 8409500x4 + 37586230x4 + 3416930x5 + 9922605x5 + 902055x6 + 1735503x6 + 157773x7 + 199650x7 + 18150x8 + (11 * 1320x8 + x * 1320x8) + 55x9 * (11 + x) + x10(11 + x))(12 + x) 0 = x(39916800 + 3628800x + 116915040x + 10628640x2 + 140289336x2 + 12753576x3 + 92504500x3 + 8409500x4 + 37586230x4 + 3416930x5 + 9922605x5 + 902055x6 + 1735503x6 + 157773x7 + 199650x7 + 18150x8 + (14520x8 + 1320x9) + 55x9 * (11 + x) + x10(11 + x))(12 + x) 0 = x(39916800 + 3628800x + 116915040x + 10628640x2 + 140289336x2 + 12753576x3 + 92504500x3 + 8409500x4 + 37586230x4 + 3416930x5 + 9922605x5 + 902055x6 + 1735503x6 + 157773x7 + 199650x7 + 18150x8 + 14520x8 + 1320x9 + (11 * 55x9 + x * 55x9) + x10(11 + x))(12 + x) 0 = x(39916800 + 3628800x + 116915040x + 10628640x2 + 140289336x2 + 12753576x3 + 92504500x3 + 8409500x4 + 37586230x4 + 3416930x5 + 9922605x5 + 902055x6 + 1735503x6 + 157773x7 + 199650x7 + 18150x8 + 14520x8 + 1320x9 + (605x9 + 55x10) + x10(11 + x))(12 + x) 0 = x(39916800 + 3628800x + 116915040x + 10628640x2 + 140289336x2 + 12753576x3 + 92504500x3 + 8409500x4 + 37586230x4 + 3416930x5 + 9922605x5 + 902055x6 + 1735503x6 + 157773x7 + 199650x7 + 18150x8 + 14520x8 + 1320x9 + 605x9 + 55x10 + (11 * x10 + x * x10))(12 + x) 0 = x(39916800 + 3628800x + 116915040x + 10628640x2 + 140289336x2 + 12753576x3 + 92504500x3 + 8409500x4 + 37586230x4 + 3416930x5 + 9922605x5 + 902055x6 + 1735503x6 + 157773x7 + 199650x7 + 18150x8 + 14520x8 + 1320x9 + 605x9 + 55x10 + (11x10 + x11))(12 + x) Combine like terms: 3628800x + 116915040x = 120543840x 0 = x(39916800 + 120543840x + 10628640x2 + 140289336x2 + 12753576x3 + 92504500x3 + 8409500x4 + 37586230x4 + 3416930x5 + 9922605x5 + 902055x6 + 1735503x6 + 157773x7 + 199650x7 + 18150x8 + 14520x8 + 1320x9 + 605x9 + 55x10 + 11x10 + x11)(12 + x) Combine like terms: 10628640x2 + 140289336x2 = 150917976x2 0 = x(39916800 + 120543840x + 150917976x2 + 12753576x3 + 92504500x3 + 8409500x4 + 37586230x4 + 3416930x5 + 9922605x5 + 902055x6 + 1735503x6 + 157773x7 + 199650x7 + 18150x8 + 14520x8 + 1320x9 + 605x9 + 55x10 + 11x10 + x11)(12 + x) Combine like terms: 12753576x3 + 92504500x3 = 105258076x3 0 = x(39916800 + 120543840x + 150917976x2 + 105258076x3 + 8409500x4 + 37586230x4 + 3416930x5 + 9922605x5 + 902055x6 + 1735503x6 + 157773x7 + 199650x7 + 18150x8 + 14520x8 + 1320x9 + 605x9 + 55x10 + 11x10 + x11)(12 + x) Combine like terms: 8409500x4 + 37586230x4 = 45995730x4 0 = x(39916800 + 120543840x + 150917976x2 + 105258076x3 + 45995730x4 + 3416930x5 + 9922605x5 + 902055x6 + 1735503x6 + 157773x7 + 199650x7 + 18150x8 + 14520x8 + 1320x9 + 605x9 + 55x10 + 11x10 + x11)(12 + x) Combine like terms: 3416930x5 + 9922605x5 = 13339535x5 0 = x(39916800 + 120543840x + 150917976x2 + 105258076x3 + 45995730x4 + 13339535x5 + 902055x6 + 1735503x6 + 157773x7 + 199650x7 + 18150x8 + 14520x8 + 1320x9 + 605x9 + 55x10 + 11x10 + x11)(12 + x) Combine like terms: 902055x6 + 1735503x6 = 2637558x6 0 = x(39916800 + 120543840x + 150917976x2 + 105258076x3 + 45995730x4 + 13339535x5 + 2637558x6 + 157773x7 + 199650x7 + 18150x8 + 14520x8 + 1320x9 + 605x9 + 55x10 + 11x10 + x11)(12 + x) Combine like terms: 157773x7 + 199650x7 = 357423x7 0 = x(39916800 + 120543840x + 150917976x2 + 105258076x3 + 45995730x4 + 13339535x5 + 2637558x6 + 357423x7 + 18150x8 + 14520x8 + 1320x9 + 605x9 + 55x10 + 11x10 + x11)(12 + x) Combine like terms: 18150x8 + 14520x8 = 32670x8 0 = x(39916800 + 120543840x + 150917976x2 + 105258076x3 + 45995730x4 + 13339535x5 + 2637558x6 + 357423x7 + 32670x8 + 1320x9 + 605x9 + 55x10 + 11x10 + x11)(12 + x) Combine like terms: 1320x9 + 605x9 = 1925x9 0 = x(39916800 + 120543840x + 150917976x2 + 105258076x3 + 45995730x4 + 13339535x5 + 2637558x6 + 357423x7 + 32670x8 + 1925x9 + 55x10 + 11x10 + x11)(12 + x) Combine like terms: 55x10 + 11x10 = 66x10 0 = x(39916800 + 120543840x + 150917976x2 + 105258076x3 + 45995730x4 + 13339535x5 + 2637558x6 + 357423x7 + 32670x8 + 1925x9 + 66x10 + x11)(12 + x) Multiply (39916800 + 120543840x + 150917976x2 + 105258076x3 + 45995730x4 + 13339535x5 + 2637558x6 + 357423x7 + 32670x8 + 1925x9 + 66x10 + x11) * (12 + x) 0 = x(39916800(12 + x) + 120543840x * (12 + x) + 150917976x2 * (12 + x) + 105258076x3 * (12 + x) + 45995730x4 * (12 + x) + 13339535x5 * (12 + x) + 2637558x6 * (12 + x) + 357423x7 * (12 + x) + 32670x8 * (12 + x) + 1925x9 * (12 + x) + 66x10 * (12 + x) + x11(12 + x)) 0 = x((12 * 39916800 + x * 39916800) + 120543840x * (12 + x) + 150917976x2 * (12 + x) + 105258076x3 * (12 + x) + 45995730x4 * (12 + x) + 13339535x5 * (12 + x) + 2637558x6 * (12 + x) + 357423x7 * (12 + x) + 32670x8 * (12 + x) + 1925x9 * (12 + x) + 66x10 * (12 + x) + x11(12 + x)) 0 = x((479001600 + 39916800x) + 120543840x * (12 + x) + 150917976x2 * (12 + x) + 105258076x3 * (12 + x) + 45995730x4 * (12 + x) + 13339535x5 * (12 + x) + 2637558x6 * (12 + x) + 357423x7 * (12 + x) + 32670x8 * (12 + x) + 1925x9 * (12 + x) + 66x10 * (12 + x) + x11(12 + x)) 0 = x(479001600 + 39916800x + (12 * 120543840x + x * 120543840x) + 150917976x2 * (12 + x) + 105258076x3 * (12 + x) + 45995730x4 * (12 + x) + 13339535x5 * (12 + x) + 2637558x6 * (12 + x) + 357423x7 * (12 + x) + 32670x8 * (12 + x) + 1925x9 * (12 + x) + 66x10 * (12 + x) + x11(12 + x)) 0 = x(479001600 + 39916800x + (1446526080x + 120543840x2) + 150917976x2 * (12 + x) + 105258076x3 * (12 + x) + 45995730x4 * (12 + x) + 13339535x5 * (12 + x) + 2637558x6 * (12 + x) + 357423x7 * (12 + x) + 32670x8 * (12 + x) + 1925x9 * (12 + x) + 66x10 * (12 + x) + x11(12 + x)) 0 = x(479001600 + 39916800x + 1446526080x + 120543840x2 + (12 * 150917976x2 + x * 150917976x2) + 105258076x3 * (12 + x) + 45995730x4 * (12 + x) + 13339535x5 * (12 + x) + 2637558x6 * (12 + x) + 357423x7 * (12 + x) + 32670x8 * (12 + x) + 1925x9 * (12 + x) + 66x10 * (12 + x) + x11(12 + x)) 0 = x(479001600 + 39916800x + 1446526080x + 120543840x2 + (1811015712x2 + 150917976x3) + 105258076x3 * (12 + x) + 45995730x4 * (12 + x) + 13339535x5 * (12 + x) + 2637558x6 * (12 + x) + 357423x7 * (12 + x) + 32670x8 * (12 + x) + 1925x9 * (12 + x) + 66x10 * (12 + x) + x11(12 + x)) 0 = x(479001600 + 39916800x + 1446526080x + 120543840x2 + 1811015712x2 + 150917976x3 + (12 * 105258076x3 + x * 105258076x3) + 45995730x4 * (12 + x) + 13339535x5 * (12 + x) + 2637558x6 * (12 + x) + 357423x7 * (12 + x) + 32670x8 * (12 + x) + 1925x9 * (12 + x) + 66x10 * (12 + x) + x11(12 + x)) 0 = x(479001600 + 39916800x + 1446526080x + 120543840x2 + 1811015712x2 + 150917976x3 + (1263096912x3 + 105258076x4) + 45995730x4 * (12 + x) + 13339535x5 * (12 + x) + 2637558x6 * (12 + x) + 357423x7 * (12 + x) + 32670x8 * (12 + x) + 1925x9 * (12 + x) + 66x10 * (12 + x) + x11(12 + x)) 0 = x(479001600 + 39916800x + 1446526080x + 120543840x2 + 1811015712x2 + 150917976x3 + 1263096912x3 + 105258076x4 + (12 * 45995730x4 + x * 45995730x4) + 13339535x5 * (12 + x) + 2637558x6 * (12 + x) + 357423x7 * (12 + x) + 32670x8 * (12 + x) + 1925x9 * (12 + x) + 66x10 * (12 + x) + x11(12 + x)) 0 = x(479001600 + 39916800x + 1446526080x + 120543840x2 + 1811015712x2 + 150917976x3 + 1263096912x3 + 105258076x4 + (551948760x4 + 45995730x5) + 13339535x5 * (12 + x) + 2637558x6 * (12 + x) + 357423x7 * (12 + x) + 32670x8 * (12 + x) + 1925x9 * (12 + x) + 66x10 * (12 + x) + x11(12 + x)) 0 = x(479001600 + 39916800x + 1446526080x + 120543840x2 + 1811015712x2 + 150917976x3 + 1263096912x3 + 105258076x4 + 551948760x4 + 45995730x5 + (12 * 13339535x5 + x * 13339535x5) + 2637558x6 * (12 + x) + 357423x7 * (12 + x) + 32670x
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