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Simplifying (x + -4)(x + 3)(2) = 120 Reorder the terms: (-4 + x)(x + 3)(2) = 120 Reorder the terms: (-4 + x)(3 + x)(2) = 120 Reorder the terms for easier multiplication: 2(-4 + x)(3 + x) = 120 Multiply (-4 + x) * (3 + x) 2(-4(3 + x) + x(3 + x)) = 120 2((3 * -4 + x * -4) + x(3 + x)) = 120 2((-12 + -4x) + x(3 + x)) = 120 2(-12 + -4x + (3 * x + x * x)) = 120 2(-12 + -4x + (3x + x2)) = 120 Combine like terms: -4x + 3x = -1x 2(-12 + -1x + x2) = 120 (-12 * 2 + -1x * 2 + x2 * 2) = 120 (-24 + -2x + 2x2) = 120 Solving -24 + -2x + 2x2 = 120 Solving for variable 'x'. Reorder the terms: -24 + -120 + -2x + 2x2 = 120 + -120 Combine like terms: -24 + -120 = -144 -144 + -2x + 2x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -144 + -2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-72 + -1x + x2) = 0 Factor a trinomial. 2((-8 + -1x)(9 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve: Simplifying -8 + -1x = 0 Solving -8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1x = 0 + 8 -1x = 0 + 8 Combine like terms: 0 + 8 = 8 -1x = 8 Divide each side by '-1'. x = -8 Simplifying x = -8Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {-8, 9}
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