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Simplifying (4x3 + -4x)(x2 + -4) = 0 Reorder the terms: (-4x + 4x3)(x2 + -4) = 0 Reorder the terms: (-4x + 4x3)(-4 + x2) = 0 Multiply (-4x + 4x3) * (-4 + x2) (-4x * (-4 + x2) + 4x3 * (-4 + x2)) = 0 ((-4 * -4x + x2 * -4x) + 4x3 * (-4 + x2)) = 0 ((16x + -4x3) + 4x3 * (-4 + x2)) = 0 (16x + -4x3 + (-4 * 4x3 + x2 * 4x3)) = 0 (16x + -4x3 + (-16x3 + 4x5)) = 0 Combine like terms: -4x3 + -16x3 = -20x3 (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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