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Simplifying (x + 1)(x + 1)(2x + 1)(2x + 1)(2x + 1)(2x + 1)(-6x + -3) = 0 Reorder the terms: (1 + x)(x + 1)(2x + 1)(2x + 1)(2x + 1)(2x + 1)(-6x + -3) = 0 Reorder the terms: (1 + x)(1 + x)(2x + 1)(2x + 1)(2x + 1)(2x + 1)(-6x + -3) = 0 Reorder the terms: (1 + x)(1 + x)(1 + 2x)(2x + 1)(2x + 1)(2x + 1)(-6x + -3) = 0 Reorder the terms: (1 + x)(1 + x)(1 + 2x)(1 + 2x)(2x + 1)(2x + 1)(-6x + -3) = 0 Reorder the terms: (1 + x)(1 + x)(1 + 2x)(1 + 2x)(1 + 2x)(2x + 1)(-6x + -3) = 0 Reorder the terms: (1 + x)(1 + x)(1 + 2x)(1 + 2x)(1 + 2x)(1 + 2x)(-6x + -3) = 0 Reorder the terms: (1 + x)(1 + x)(1 + 2x)(1 + 2x)(1 + 2x)(1 + 2x)(-3 + -6x) = 0 Multiply (1 + x) * (1 + x) (1(1 + x) + x(1 + x))(1 + 2x)(1 + 2x)(1 + 2x)(1 + 2x)(-3 + -6x) = 0 ((1 * 1 + x * 1) + x(1 + x))(1 + 2x)(1 + 2x)(1 + 2x)(1 + 2x)(-3 + -6x) = 0 ((1 + 1x) + x(1 + x))(1 + 2x)(1 + 2x)(1 + 2x)(1 + 2x)(-3 + -6x) = 0 (1 + 1x + (1 * x + x * x))(1 + 2x)(1 + 2x)(1 + 2x)(1 + 2x)(-3 + -6x) = 0 (1 + 1x + (1x + x2))(1 + 2x)(1 + 2x)(1 + 2x)(1 + 2x)(-3 + -6x) = 0 Combine like terms: 1x + 1x = 2x (1 + 2x + x2)(1 + 2x)(1 + 2x)(1 + 2x)(1 + 2x)(-3 + -6x) = 0 Multiply (1 + 2x + x2) * (1 + 2x) (1(1 + 2x) + 2x * (1 + 2x) + x2(1 + 2x))(1 + 2x)(1 + 2x)(1 + 2x)(-3 + -6x) = 0 ((1 * 1 + 2x * 1) + 2x * (1 + 2x) + x2(1 + 2x))(1 + 2x)(1 + 2x)(1 + 2x)(-3 + -6x) = 0 ((1 + 2x) + 2x * (1 + 2x) + x2(1 + 2x))(1 + 2x)(1 + 2x)(1 + 2x)(-3 + -6x) = 0 (1 + 2x + (1 * 2x + 2x * 2x) + x2(1 + 2x))(1 + 2x)(1 + 2x)(1 + 2x)(-3 + -6x) = 0 (1 + 2x + (2x + 4x2) + x2(1 + 2x))(1 + 2x)(1 + 2x)(1 + 2x)(-3 + -6x) = 0 (1 + 2x + 2x + 4x2 + (1 * x2 + 2x * x2))(1 + 2x)(1 + 2x)(1 + 2x)(-3 + -6x) = 0 (1 + 2x + 2x + 4x2 + (1x2 + 2x3))(1 + 2x)(1 + 2x)(1 + 2x)(-3 + -6x) = 0 Combine like terms: 2x + 2x = 4x (1 + 4x + 4x2 + 1x2 + 2x3)(1 + 2x)(1 + 2x)(1 + 2x)(-3 + -6x) = 0 Combine like terms: 4x2 + 1x2 = 5x2 (1 + 4x + 5x2 + 2x3)(1 + 2x)(1 + 2x)(1 + 2x)(-3 + -6x) = 0 Multiply (1 + 4x + 5x2 + 2x3) * (1 + 2x) (1(1 + 2x) + 4x * (1 + 2x) + 5x2 * (1 + 2x) + 2x3 * (1 + 2x))(1 + 2x)(1 + 2x)(-3 + -6x) = 0 ((1 * 1 + 2x * 1) + 4x * (1 + 2x) + 5x2 * (1 + 2x) + 2x3 * (1 + 2x))(1 + 2x)(1 + 2x)(-3 + -6x) = 0 ((1 + 2x) + 4x * (1 + 2x) + 5x2 * (1 + 2x) + 2x3 * (1 + 2x))(1 + 2x)(1 + 2x)(-3 + -6x) = 0 (1 + 2x + (1 * 4x + 2x * 4x) + 5x2 * (1 + 2x) + 2x3 * (1 + 2x))(1 + 2x)(1 + 2x)(-3 + -6x) = 0 (1 + 2x + (4x + 8x2) + 5x2 * (1 + 2x) + 2x3 * (1 + 2x))(1 + 2x)(1 + 2x)(-3 + -6x) = 0 (1 + 2x + 4x + 8x2 + (1 * 5x2 + 2x * 5x2) + 2x3 * (1 + 2x))(1 + 2x)(1 + 2x)(-3 + -6x) = 0 (1 + 2x + 4x + 8x2 + (5x2 + 10x3) + 2x3 * (1 + 2x))(1 + 2x)(1 + 2x)(-3 + -6x) = 0 (1 + 2x + 4x + 8x2 + 5x2 + 10x3 + (1 * 2x3 + 2x * 2x3))(1 + 2x)(1 + 2x)(-3 + -6x) = 0 (1 + 2x + 4x + 8x2 + 5x2 + 10x3 + (2x3 + 4x4))(1 + 2x)(1 + 2x)(-3 + -6x) = 0 Combine like terms: 2x + 4x = 6x (1 + 6x + 8x2 + 5x2 + 10x3 + 2x3 + 4x4)(1 + 2x)(1 + 2x)(-3 + -6x) = 0 Combine like terms: 8x2 + 5x2 = 13x2 (1 + 6x + 13x2 + 10x3 + 2x3 + 4x4)(1 + 2x)(1 + 2x)(-3 + -6x) = 0 Combine like terms: 10x3 + 2x3 = 12x3 (1 + 6x + 13x2 + 12x3 + 4x4)(1 + 2x)(1 + 2x)(-3 + -6x) = 0 Multiply (1 + 6x + 13x2 + 12x3 + 4x4) * (1 + 2x) (1(1 + 2x) + 6x * (1 + 2x) + 13x2 * (1 + 2x) + 12x3 * (1 + 2x) + 4x4 * (1 + 2x))(1 + 2x)(-3 + -6x) = 0 ((1 * 1 + 2x * 1) + 6x * (1 + 2x) + 13x2 * (1 + 2x) + 12x3 * (1 + 2x) + 4x4 * (1 + 2x))(1 + 2x)(-3 + -6x) = 0 ((1 + 2x) + 6x * (1 + 2x) + 13x2 * (1 + 2x) + 12x3 * (1 + 2x) + 4x4 * (1 + 2x))(1 + 2x)(-3 + -6x) = 0 (1 + 2x + (1 * 6x + 2x * 6x) + 13x2 * (1 + 2x) + 12x3 * (1 + 2x) + 4x4 * (1 + 2x))(1 + 2x)(-3 + -6x) = 0 (1 + 2x + (6x + 12x2) + 13x2 * (1 + 2x) + 12x3 * (1 + 2x) + 4x4 * (1 + 2x))(1 + 2x)(-3 + -6x) = 0 (1 + 2x + 6x + 12x2 + (1 * 13x2 + 2x * 13x2) + 12x3 * (1 + 2x) + 4x4 * (1 + 2x))(1 + 2x)(-3 + -6x) = 0 (1 + 2x + 6x + 12x2 + (13x2 + 26x3) + 12x3 * (1 + 2x) + 4x4 * (1 + 2x))(1 + 2x)(-3 + -6x) = 0 (1 + 2x + 6x + 12x2 + 13x2 + 26x3 + (1 * 12x3 + 2x * 12x3) + 4x4 * (1 + 2x))(1 + 2x)(-3 + -6x) = 0 (1 + 2x + 6x + 12x2 + 13x2 + 26x3 + (12x3 + 24x4) + 4x4 * (1 + 2x))(1 + 2x)(-3 + -6x) = 0 (1 + 2x + 6x + 12x2 + 13x2 + 26x3 + 12x3 + 24x4 + (1 * 4x4 + 2x * 4x4))(1 + 2x)(-3 + -6x) = 0 (1 + 2x + 6x + 12x2 + 13x2 + 26x3 + 12x3 + 24x4 + (4x4 + 8x5))(1 + 2x)(-3 + -6x) = 0 Combine like terms: 2x + 6x = 8x (1 + 8x + 12x2 + 13x2 + 26x3 + 12x3 + 24x4 + 4x4 + 8x5)(1 + 2x)(-3 + -6x) = 0 Combine like terms: 12x2 + 13x2 = 25x2 (1 + 8x + 25x2 + 26x3 + 12x3 + 24x4 + 4x4 + 8x5)(1 + 2x)(-3 + -6x) = 0 Combine like terms: 26x3 + 12x3 = 38x3 (1 + 8x + 25x2 + 38x3 + 24x4 + 4x4 + 8x5)(1 + 2x)(-3 + -6x) = 0 Combine like terms: 24x4 + 4x4 = 28x4 (1 + 8x + 25x2 + 38x3 + 28x4 + 8x5)(1 + 2x)(-3 + -6x) = 0 Multiply (1 + 8x + 25x2 + 38x3 + 28x4 + 8x5) * (1 + 2x) (1(1 + 2x) + 8x * (1 + 2x) + 25x2 * (1 + 2x) + 38x3 * (1 + 2x) + 28x4 * (1 + 2x) + 8x5 * (1 + 2x))(-3 + -6x) = 0 ((1 * 1 + 2x * 1) + 8x * (1 + 2x) + 25x2 * (1 + 2x) + 38x3 * (1 + 2x) + 28x4 * (1 + 2x) + 8x5 * (1 + 2x))(-3 + -6x) = 0 ((1 + 2x) + 8x * (1 + 2x) + 25x2 * (1 + 2x) + 38x3 * (1 + 2x) + 28x4 * (1 + 2x) + 8x5 * (1 + 2x))(-3 + -6x) = 0 (1 + 2x + (1 * 8x + 2x * 8x) + 25x2 * (1 + 2x) + 38x3 * (1 + 2x) + 28x4 * (1 + 2x) + 8x5 * (1 + 2x))(-3 + -6x) = 0 (1 + 2x + (8x + 16x2) + 25x2 * (1 + 2x) + 38x3 * (1 + 2x) + 28x4 * (1 + 2x) + 8x5 * (1 + 2x))(-3 + -6x) = 0 (1 + 2x + 8x + 16x2 + (1 * 25x2 + 2x * 25x2) + 38x3 * (1 + 2x) + 28x4 * (1 + 2x) + 8x5 * (1 + 2x))(-3 + -6x) = 0 (1 + 2x + 8x + 16x2 + (25x2 + 50x3) + 38x3 * (1 + 2x) + 28x4 * (1 + 2x) + 8x5 * (1 + 2x))(-3 + -6x) = 0 (1 + 2x + 8x + 16x2 + 25x2 + 50x3 + (1 * 38x3 + 2x * 38x3) + 28x4 * (1 + 2x) + 8x5 * (1 + 2x))(-3 + -6x) = 0 (1 + 2x + 8x + 16x2 + 25x2 + 50x3 + (38x3 + 76x4) + 28x4 * (1 + 2x) + 8x5 * (1 + 2x))(-3 + -6x) = 0 (1 + 2x + 8x + 16x2 + 25x2 + 50x3 + 38x3 + 76x4 + (1 * 28x4 + 2x * 28x4) + 8x5 * (1 + 2x))(-3 + -6x) = 0 (1 + 2x + 8x + 16x2 + 25x2 + 50x3 + 38x3 + 76x4 + (28x4 + 56x5) + 8x5 * (1 + 2x))(-3 + -6x) = 0 (1 + 2x + 8x + 16x2 + 25x2 + 50x3 + 38x3 + 76x4 + 28x4 + 56x5 + (1 * 8x5 + 2x * 8x5))(-3 + -6x) = 0 (1 + 2x + 8x + 16x2 + 25x2 + 50x3 + 38x3 + 76x4 + 28x4 + 56x5 + (8x5 + 16x6))(-3 + -6x) = 0 Combine like terms: 2x + 8x = 10x (1 + 10x + 16x2 + 25x2 + 50x3 + 38x3 + 76x4 + 28x4 + 56x5 + 8x5 + 16x6)(-3 + -6x) = 0 Combine like terms: 16x2 + 25x2 = 41x2 (1 + 10x + 41x2 + 50x3 + 38x3 + 76x4 + 28x4 + 56x5 + 8x5 + 16x6)(-3 + -6x) = 0 Combine like terms: 50x3 + 38x3 = 88x3 (1 + 10x + 41x2 + 88x3 + 76x4 + 28x4 + 56x5 + 8x5 + 16x6)(-3 + -6x) = 0 Combine like terms: 76x4 + 28x4 = 104x4 (1 + 10x + 41x2 + 88x3 + 104x4 + 56x5 + 8x5 + 16x6)(-3 + -6x) = 0 Combine like terms: 56x5 + 8x5 = 64x5 (1 + 10x + 41x2 + 88x3 + 104x4 + 64x5 + 16x6)(-3 + -6x) = 0 Multiply (1 + 10x + 41x2 + 88x3 + 104x4 + 64x5 + 16x6) * (-3 + -6x) (1(-3 + -6x) + 10x * (-3 + -6x) + 41x2 * (-3 + -6x) + 88x3 * (-3 + -6x) + 104x4 * (-3 + -6x) + 64x5 * (-3 + -6x) + 16x6 * (-3 + -6x)) = 0 ((-3 * 1 + -6x * 1) + 10x * (-3 + -6x) + 41x2 * (-3 + -6x) + 88x3 * (-3 + -6x) + 104x4 * (-3 + -6x) + 64x5 * (-3 + -6x) + 16x6 * (-3 + -6x)) = 0 ((-3 + -6x) + 10x * (-3 + -6x) + 41x2 * (-3 + -6x) + 88x3 * (-3 + -6x) + 104x4 * (-3 + -6x) + 64x5 * (-3 + -6x) + 16x6 * (-3 + -6x)) = 0 (-3 + -6x + (-3 * 10x + -6x * 10x) + 41x2 * (-3 + -6x) + 88x3 * (-3 + -6x) + 104x4 * (-3 + -6x) + 64x5 * (-3 + -6x) + 16x6 * (-3 + -6x)) = 0 (-3 + -6x + (-30x + -60x2) + 41x2 * (-3 + -6x) + 88x3 * (-3 + -6x) + 104x4 * (-3 + -6x) + 64x5 * (-3 + -6x) + 16x6 * (-3 + -6x)) = 0 (-3 + -6x + -30x + -60x2 + (-3 * 41x2 + -6x * 41x2) + 88x3 * (-3 + -6x) + 104x4 * (-3 + -6x) + 64x5 * (-3 + -6x) + 16x6 * (-3 + -6x)) = 0 (-3 + -6x + -30x + -60x2 + (-123x2 + -246x3) + 88x3 * (-3 + -6x) + 104x4 * (-3 + -6x) + 64x5 * (-3 + -6x) + 16x6 * (-3 + -6x)) = 0 (-3 + -6x + -30x + -60x2 + -123x2 + -246x3 + (-3 * 88x3 + -6x * 88x3) + 104x4 * (-3 + -6x) + 64x5 * (-3 + -6x) + 16x6 * (-3 + -6x)) = 0 (-3 + -6x + -30x + -60x2 + -123x2 + -246x3 + (-264x3 + -528x4) + 104x4 * (-3 + -6x) + 64x5 * (-3 + -6x) + 16x6 * (-3 + -6x)) = 0 (-3 + -6x + -30x + -60x2 + -123x2 + -246x3 + -264x3 + -528x4 + (-3 * 104x4 + -6x * 104x4) + 64x5 * (-3 + -6x) + 16x6 * (-3 + -6x)) = 0 (-3 + -6x + -30x + -60x2 + -123x2 + -246x3 + -264x3 + -528x4 + (-312x4 + -624x5) + 64x5 * (-3 + -6x) + 16x6 * (-3 + -6x)) = 0 (-3 + -6x + -30x + -60x2 + -123x2 + -246x3 + -264x3 + -528x4 + -312x4 + -624x5 + (-3 * 64x5 + -6x * 64x5) + 16x6 * (-3 + -6x)) = 0 (-3 + -6x + -30x + -60x2 + -123x2 + -246x3 + -264x3 + -528x4 + -312x4 + -624x5 + (-192x5 + -384x6) + 16x6 * (-3 + -6x)) = 0 (-3 + -6x + -30x + -60x2 + -123x2 + -246x3 + -264x3 + -528x4 + -312x4 + -624x5 + -192x5 + -384x6 + (-3 * 16x6 + -6x * 16x6)) = 0 (-3 + -6x + -30x + -60x2 + -123x2 + -246x3 + -264x3 + -528x4 + -312x4 + -624x5 + -192x5 + -384x6 + (-48x6 + -96x7)) = 0 Combine like terms: -6x + -30x = -36x (-3 + -36x + -60x2 + -123x2 + -246x3 + -264x3 + -528x4 + -312x4 + -624x5 + -192x5 + -384x6 + -48x6 + -96x7) = 0 Combine like terms: -60x2 + -123x2 = -183x2 (-3 + -36x + -183x2 + -246x3 + -264x3 + -528x4 + -312x4 + -624x5 + -192x5 + -384x6 + -48x6 + -96x7) = 0 Combine like terms: -246x3 + -264x3 = -510x3 (-3 + -36x + -183x2 + -510x3 + -528x4 + -312x4 + -624x5 + -192x5 + -384x6 + -48x6 + -96x7) = 0 Combine like terms: -528x4 + -312x4 = -840x4 (-3 + -36x + -183x2 + -510x3 + -840x4 + -624x5 + -192x5 + -384x6 + -48x6 + -96x7) = 0 Combine like terms: -624x5 + -192x5 = -816x5 (-3 + -36x + -183x2 + -510x3 + -840x4 + -816x5 + -384x6 + -48x6 + -96x7) = 0 Combine like terms: -384x6 + -48x6 = -432x6 (-3 + -36x + -183x2 + -510x3 + -840x4 + -816x5 + -432x6 + -96x7) = 0 Solving -3 + -36x + -183x2 + -510x3 + -840x4 + -816x5 + -432x6 + -96x7 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-3'. -3(1 + 12x + 61x2 + 170x3 + 280x4 + 272x5 + 144x6 + 32x7) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(1 + 12x + 61x2 + 170x3 + 280x4 + 272x5 + 144x6 + 32x7)' equal to zero and attempt to solve: Simplifying 1 + 12x + 61x2 + 170x3 + 280x4 + 272x5 + 144x6 + 32x7 = 0 Solving 1 + 12x + 61x2 + 170x3 + 280x4 + 272x5 + 144x6 + 32x7 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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