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Simplifying (x + 2)(x + 3)(x + 4)(x + 1) = 24 Reorder the terms: (2 + x)(x + 3)(x + 4)(x + 1) = 24 Reorder the terms: (2 + x)(3 + x)(x + 4)(x + 1) = 24 Reorder the terms: (2 + x)(3 + x)(4 + x)(x + 1) = 24 Reorder the terms: (2 + x)(3 + x)(4 + x)(1 + x) = 24 Multiply (2 + x) * (3 + x) (2(3 + x) + x(3 + x))(4 + x)(1 + x) = 24 ((3 * 2 + x * 2) + x(3 + x))(4 + x)(1 + x) = 24 ((6 + 2x) + x(3 + x))(4 + x)(1 + x) = 24 (6 + 2x + (3 * x + x * x))(4 + x)(1 + x) = 24 (6 + 2x + (3x + x2))(4 + x)(1 + x) = 24 Combine like terms: 2x + 3x = 5x (6 + 5x + x2)(4 + x)(1 + x) = 24 Multiply (6 + 5x + x2) * (4 + x) (6(4 + x) + 5x * (4 + x) + x2(4 + x))(1 + x) = 24 ((4 * 6 + x * 6) + 5x * (4 + x) + x2(4 + x))(1 + x) = 24 ((24 + 6x) + 5x * (4 + x) + x2(4 + x))(1 + x) = 24 (24 + 6x + (4 * 5x + x * 5x) + x2(4 + x))(1 + x) = 24 (24 + 6x + (20x + 5x2) + x2(4 + x))(1 + x) = 24 (24 + 6x + 20x + 5x2 + (4 * x2 + x * x2))(1 + x) = 24 (24 + 6x + 20x + 5x2 + (4x2 + x3))(1 + x) = 24 Combine like terms: 6x + 20x = 26x (24 + 26x + 5x2 + 4x2 + x3)(1 + x) = 24 Combine like terms: 5x2 + 4x2 = 9x2 (24 + 26x + 9x2 + x3)(1 + x) = 24 Multiply (24 + 26x + 9x2 + x3) * (1 + x) (24(1 + x) + 26x * (1 + x) + 9x2 * (1 + x) + x3(1 + x)) = 24 ((1 * 24 + x * 24) + 26x * (1 + x) + 9x2 * (1 + x) + x3(1 + x)) = 24 ((24 + 24x) + 26x * (1 + x) + 9x2 * (1 + x) + x3(1 + x)) = 24 (24 + 24x + (1 * 26x + x * 26x) + 9x2 * (1 + x) + x3(1 + x)) = 24 (24 + 24x + (26x + 26x2) + 9x2 * (1 + x) + x3(1 + x)) = 24 (24 + 24x + 26x + 26x2 + (1 * 9x2 + x * 9x2) + x3(1 + x)) = 24 (24 + 24x + 26x + 26x2 + (9x2 + 9x3) + x3(1 + x)) = 24 (24 + 24x + 26x + 26x2 + 9x2 + 9x3 + (1 * x3 + x * x3)) = 24 (24 + 24x + 26x + 26x2 + 9x2 + 9x3 + (1x3 + x4)) = 24 Combine like terms: 24x + 26x = 50x (24 + 50x + 26x2 + 9x2 + 9x3 + 1x3 + x4) = 24 Combine like terms: 26x2 + 9x2 = 35x2 (24 + 50x + 35x2 + 9x3 + 1x3 + x4) = 24 Combine like terms: 9x3 + 1x3 = 10x3 (24 + 50x + 35x2 + 10x3 + x4) = 24 Add '-24' to each side of the equation. 24 + 50x + 35x2 + 10x3 + -24 + x4 = 24 + -24 Reorder the terms: 24 + -24 + 50x + 35x2 + 10x3 + x4 = 24 + -24 Combine like terms: 24 + -24 = 0 0 + 50x + 35x2 + 10x3 + x4 = 24 + -24 50x + 35x2 + 10x3 + x4 = 24 + -24 Combine like terms: 24 + -24 = 0 50x + 35x2 + 10x3 + x4 = 0 Solving 50x + 35x2 + 10x3 + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(50 + 35x + 10x2 + 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 '(50 + 35x + 10x2 + x3)' equal to zero and attempt to solve: Simplifying 50 + 35x + 10x2 + x3 = 0 Solving 50 + 35x + 10x2 + 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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