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Simplifying (x3 + -1x2 + -2x)(4x2 + 4x + -8) = 0 Reorder the terms: (-2x + -1x2 + x3)(4x2 + 4x + -8) = 0 Reorder the terms: (-2x + -1x2 + x3)(-8 + 4x + 4x2) = 0 Multiply (-2x + -1x2 + x3) * (-8 + 4x + 4x2) (-2x * (-8 + 4x + 4x2) + -1x2 * (-8 + 4x + 4x2) + x3(-8 + 4x + 4x2)) = 0 ((-8 * -2x + 4x * -2x + 4x2 * -2x) + -1x2 * (-8 + 4x + 4x2) + x3(-8 + 4x + 4x2)) = 0 ((16x + -8x2 + -8x3) + -1x2 * (-8 + 4x + 4x2) + x3(-8 + 4x + 4x2)) = 0 (16x + -8x2 + -8x3 + (-8 * -1x2 + 4x * -1x2 + 4x2 * -1x2) + x3(-8 + 4x + 4x2)) = 0 (16x + -8x2 + -8x3 + (8x2 + -4x3 + -4x4) + x3(-8 + 4x + 4x2)) = 0 (16x + -8x2 + -8x3 + 8x2 + -4x3 + -4x4 + (-8 * x3 + 4x * x3 + 4x2 * x3)) = 0 (16x + -8x2 + -8x3 + 8x2 + -4x3 + -4x4 + (-8x3 + 4x4 + 4x5)) = 0 Reorder the terms: (16x + -8x2 + 8x2 + -8x3 + -4x3 + -8x3 + -4x4 + 4x4 + 4x5) = 0 Combine like terms: -8x2 + 8x2 = 0 (16x + 0 + -8x3 + -4x3 + -8x3 + -4x4 + 4x4 + 4x5) = 0 (16x + -8x3 + -4x3 + -8x3 + -4x4 + 4x4 + 4x5) = 0 Combine like terms: -8x3 + -4x3 = -12x3 (16x + -12x3 + -8x3 + -4x4 + 4x4 + 4x5) = 0 Combine like terms: -12x3 + -8x3 = -20x3 (16x + -20x3 + -4x4 + 4x4 + 4x5) = 0 Combine like terms: -4x4 + 4x4 = 0 (16x + -20x3 + 0 + 4x5) = 0 (16x + -20x3 + 4x5) = 0 Solving 16x + -20x3 + 4x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(4 + -5x2 + x4) = 0 Factor a trinomial. 4x((1 + -1x2)(4 + -1x2)) = 0 Factor a difference between two squares. 4x(((1 + x)(1 + -1x))(4 + -1x2)) = 0 Factor a difference between two squares. 4x(((2 + x)(2 + -1x))(1 + x)(1 + -1x)) = 0 Ignore the factor 4.Subproblem 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 4
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 5
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 = 2Solution
x = {0, -1, 1, -2, 2}
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