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Simplifying x(x + 4)(x + -1) = 2x(x + 4) Reorder the terms: x(4 + x)(x + -1) = 2x(x + 4) Reorder the terms: x(4 + x)(-1 + x) = 2x(x + 4) Multiply (4 + x) * (-1 + x) x(4(-1 + x) + x(-1 + x)) = 2x(x + 4) x((-1 * 4 + x * 4) + x(-1 + x)) = 2x(x + 4) x((-4 + 4x) + x(-1 + x)) = 2x(x + 4) x(-4 + 4x + (-1 * x + x * x)) = 2x(x + 4) x(-4 + 4x + (-1x + x2)) = 2x(x + 4) Combine like terms: 4x + -1x = 3x x(-4 + 3x + x2) = 2x(x + 4) (-4 * x + 3x * x + x2 * x) = 2x(x + 4) (-4x + 3x2 + x3) = 2x(x + 4) Reorder the terms: -4x + 3x2 + x3 = 2x(4 + x) -4x + 3x2 + x3 = (4 * 2x + x * 2x) -4x + 3x2 + x3 = (8x + 2x2) Solving -4x + 3x2 + x3 = 8x + 2x2 Solving for variable 'x'. Reorder the terms: -4x + -8x + 3x2 + -2x2 + x3 = 8x + 2x2 + -8x + -2x2 Combine like terms: -4x + -8x = -12x -12x + 3x2 + -2x2 + x3 = 8x + 2x2 + -8x + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 -12x + 1x2 + x3 = 8x + 2x2 + -8x + -2x2 Reorder the terms: -12x + 1x2 + x3 = 8x + -8x + 2x2 + -2x2 Combine like terms: 8x + -8x = 0 -12x + 1x2 + x3 = 0 + 2x2 + -2x2 -12x + 1x2 + x3 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -12x + 1x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-12 + x + x2) = 0 Factor a trinomial. x((-4 + -1x)(3 + -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 '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {0, -4, 3}
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