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Simplifying (x + -2)(x + 3)(x + -4) = 24 Reorder the terms: (-2 + x)(x + 3)(x + -4) = 24 Reorder the terms: (-2 + x)(3 + x)(x + -4) = 24 Reorder the terms: (-2 + x)(3 + x)(-4 + x) = 24 Multiply (-2 + x) * (3 + x) (-2(3 + x) + x(3 + x))(-4 + x) = 24 ((3 * -2 + x * -2) + x(3 + x))(-4 + x) = 24 ((-6 + -2x) + x(3 + x))(-4 + x) = 24 (-6 + -2x + (3 * x + x * x))(-4 + x) = 24 (-6 + -2x + (3x + x2))(-4 + x) = 24 Combine like terms: -2x + 3x = 1x (-6 + 1x + x2)(-4 + x) = 24 Multiply (-6 + 1x + x2) * (-4 + x) (-6(-4 + x) + 1x * (-4 + x) + x2(-4 + x)) = 24 ((-4 * -6 + x * -6) + 1x * (-4 + x) + x2(-4 + x)) = 24 ((24 + -6x) + 1x * (-4 + x) + x2(-4 + x)) = 24 (24 + -6x + (-4 * 1x + x * 1x) + x2(-4 + x)) = 24 (24 + -6x + (-4x + 1x2) + x2(-4 + x)) = 24 (24 + -6x + -4x + 1x2 + (-4 * x2 + x * x2)) = 24 (24 + -6x + -4x + 1x2 + (-4x2 + x3)) = 24 Combine like terms: -6x + -4x = -10x (24 + -10x + 1x2 + -4x2 + x3) = 24 Combine like terms: 1x2 + -4x2 = -3x2 (24 + -10x + -3x2 + x3) = 24 Add '-24' to each side of the equation. 24 + -10x + -3x2 + -24 + x3 = 24 + -24 Reorder the terms: 24 + -24 + -10x + -3x2 + x3 = 24 + -24 Combine like terms: 24 + -24 = 0 0 + -10x + -3x2 + x3 = 24 + -24 -10x + -3x2 + x3 = 24 + -24 Combine like terms: 24 + -24 = 0 -10x + -3x2 + x3 = 0 Solving -10x + -3x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-10 + -3x + x2) = 0 Factor a trinomial. x((-2 + -1x)(5 + -1x)) = 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 '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {0, -2, 5}
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