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Simplifying (x + 1)(x + 3)(x + 2)(x + 4) + 1 = 0 Reorder the terms: (1 + x)(x + 3)(x + 2)(x + 4) + 1 = 0 Reorder the terms: (1 + x)(3 + x)(x + 2)(x + 4) + 1 = 0 Reorder the terms: (1 + x)(3 + x)(2 + x)(x + 4) + 1 = 0 Reorder the terms: (1 + x)(3 + x)(2 + x)(4 + x) + 1 = 0 Multiply (1 + x) * (3 + x) (1(3 + x) + x(3 + x))(2 + x)(4 + x) + 1 = 0 ((3 * 1 + x * 1) + x(3 + x))(2 + x)(4 + x) + 1 = 0 ((3 + 1x) + x(3 + x))(2 + x)(4 + x) + 1 = 0 (3 + 1x + (3 * x + x * x))(2 + x)(4 + x) + 1 = 0 (3 + 1x + (3x + x2))(2 + x)(4 + x) + 1 = 0 Combine like terms: 1x + 3x = 4x (3 + 4x + x2)(2 + x)(4 + x) + 1 = 0 Multiply (3 + 4x + x2) * (2 + x) (3(2 + x) + 4x * (2 + x) + x2(2 + x))(4 + x) + 1 = 0 ((2 * 3 + x * 3) + 4x * (2 + x) + x2(2 + x))(4 + x) + 1 = 0 ((6 + 3x) + 4x * (2 + x) + x2(2 + x))(4 + x) + 1 = 0 (6 + 3x + (2 * 4x + x * 4x) + x2(2 + x))(4 + x) + 1 = 0 (6 + 3x + (8x + 4x2) + x2(2 + x))(4 + x) + 1 = 0 (6 + 3x + 8x + 4x2 + (2 * x2 + x * x2))(4 + x) + 1 = 0 (6 + 3x + 8x + 4x2 + (2x2 + x3))(4 + x) + 1 = 0 Combine like terms: 3x + 8x = 11x (6 + 11x + 4x2 + 2x2 + x3)(4 + x) + 1 = 0 Combine like terms: 4x2 + 2x2 = 6x2 (6 + 11x + 6x2 + x3)(4 + x) + 1 = 0 Multiply (6 + 11x + 6x2 + x3) * (4 + x) (6(4 + x) + 11x * (4 + x) + 6x2 * (4 + x) + x3(4 + x)) + 1 = 0 ((4 * 6 + x * 6) + 11x * (4 + x) + 6x2 * (4 + x) + x3(4 + x)) + 1 = 0 ((24 + 6x) + 11x * (4 + x) + 6x2 * (4 + x) + x3(4 + x)) + 1 = 0 (24 + 6x + (4 * 11x + x * 11x) + 6x2 * (4 + x) + x3(4 + x)) + 1 = 0 (24 + 6x + (44x + 11x2) + 6x2 * (4 + x) + x3(4 + x)) + 1 = 0 (24 + 6x + 44x + 11x2 + (4 * 6x2 + x * 6x2) + x3(4 + x)) + 1 = 0 (24 + 6x + 44x + 11x2 + (24x2 + 6x3) + x3(4 + x)) + 1 = 0 (24 + 6x + 44x + 11x2 + 24x2 + 6x3 + (4 * x3 + x * x3)) + 1 = 0 (24 + 6x + 44x + 11x2 + 24x2 + 6x3 + (4x3 + x4)) + 1 = 0 Combine like terms: 6x + 44x = 50x (24 + 50x + 11x2 + 24x2 + 6x3 + 4x3 + x4) + 1 = 0 Combine like terms: 11x2 + 24x2 = 35x2 (24 + 50x + 35x2 + 6x3 + 4x3 + x4) + 1 = 0 Combine like terms: 6x3 + 4x3 = 10x3 (24 + 50x + 35x2 + 10x3 + x4) + 1 = 0 Reorder the terms: 24 + 1 + 50x + 35x2 + 10x3 + x4 = 0 Combine like terms: 24 + 1 = 25 25 + 50x + 35x2 + 10x3 + x4 = 0 Solving 25 + 50x + 35x2 + 10x3 + x4 = 0 Solving for variable 'x'. The solution to this equation could not be determined.
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