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Simplifying (x + 1)(x + 3)(x + 4)(x + 6) = 72 Reorder the terms: (1 + x)(x + 3)(x + 4)(x + 6) = 72 Reorder the terms: (1 + x)(3 + x)(x + 4)(x + 6) = 72 Reorder the terms: (1 + x)(3 + x)(4 + x)(x + 6) = 72 Reorder the terms: (1 + x)(3 + x)(4 + x)(6 + x) = 72 Multiply (1 + x) * (3 + x) (1(3 + x) + x(3 + x))(4 + x)(6 + x) = 72 ((3 * 1 + x * 1) + x(3 + x))(4 + x)(6 + x) = 72 ((3 + 1x) + x(3 + x))(4 + x)(6 + x) = 72 (3 + 1x + (3 * x + x * x))(4 + x)(6 + x) = 72 (3 + 1x + (3x + x2))(4 + x)(6 + x) = 72 Combine like terms: 1x + 3x = 4x (3 + 4x + x2)(4 + x)(6 + x) = 72 Multiply (3 + 4x + x2) * (4 + x) (3(4 + x) + 4x * (4 + x) + x2(4 + x))(6 + x) = 72 ((4 * 3 + x * 3) + 4x * (4 + x) + x2(4 + x))(6 + x) = 72 ((12 + 3x) + 4x * (4 + x) + x2(4 + x))(6 + x) = 72 (12 + 3x + (4 * 4x + x * 4x) + x2(4 + x))(6 + x) = 72 (12 + 3x + (16x + 4x2) + x2(4 + x))(6 + x) = 72 (12 + 3x + 16x + 4x2 + (4 * x2 + x * x2))(6 + x) = 72 (12 + 3x + 16x + 4x2 + (4x2 + x3))(6 + x) = 72 Combine like terms: 3x + 16x = 19x (12 + 19x + 4x2 + 4x2 + x3)(6 + x) = 72 Combine like terms: 4x2 + 4x2 = 8x2 (12 + 19x + 8x2 + x3)(6 + x) = 72 Multiply (12 + 19x + 8x2 + x3) * (6 + x) (12(6 + x) + 19x * (6 + x) + 8x2 * (6 + x) + x3(6 + x)) = 72 ((6 * 12 + x * 12) + 19x * (6 + x) + 8x2 * (6 + x) + x3(6 + x)) = 72 ((72 + 12x) + 19x * (6 + x) + 8x2 * (6 + x) + x3(6 + x)) = 72 (72 + 12x + (6 * 19x + x * 19x) + 8x2 * (6 + x) + x3(6 + x)) = 72 (72 + 12x + (114x + 19x2) + 8x2 * (6 + x) + x3(6 + x)) = 72 (72 + 12x + 114x + 19x2 + (6 * 8x2 + x * 8x2) + x3(6 + x)) = 72 (72 + 12x + 114x + 19x2 + (48x2 + 8x3) + x3(6 + x)) = 72 (72 + 12x + 114x + 19x2 + 48x2 + 8x3 + (6 * x3 + x * x3)) = 72 (72 + 12x + 114x + 19x2 + 48x2 + 8x3 + (6x3 + x4)) = 72 Combine like terms: 12x + 114x = 126x (72 + 126x + 19x2 + 48x2 + 8x3 + 6x3 + x4) = 72 Combine like terms: 19x2 + 48x2 = 67x2 (72 + 126x + 67x2 + 8x3 + 6x3 + x4) = 72 Combine like terms: 8x3 + 6x3 = 14x3 (72 + 126x + 67x2 + 14x3 + x4) = 72 Add '-72' to each side of the equation. 72 + 126x + 67x2 + 14x3 + -72 + x4 = 72 + -72 Reorder the terms: 72 + -72 + 126x + 67x2 + 14x3 + x4 = 72 + -72 Combine like terms: 72 + -72 = 0 0 + 126x + 67x2 + 14x3 + x4 = 72 + -72 126x + 67x2 + 14x3 + x4 = 72 + -72 Combine like terms: 72 + -72 = 0 126x + 67x2 + 14x3 + x4 = 0 Solving 126x + 67x2 + 14x3 + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(126 + 67x + 14x2 + x3) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(126 + 67x + 14x2 + x3)' equal to zero and attempt to solve: Simplifying 126 + 67x + 14x2 + x3 = 0 Solving 126 + 67x + 14x2 + x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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