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Simplifying (2x + 4)(x2 + -2x) = 0 Reorder the terms: (4 + 2x)(x2 + -2x) = 0 Reorder the terms: (4 + 2x)(-2x + x2) = 0 Multiply (4 + 2x) * (-2x + x2) (4(-2x + x2) + 2x * (-2x + x2)) = 0 ((-2x * 4 + x2 * 4) + 2x * (-2x + x2)) = 0 ((-8x + 4x2) + 2x * (-2x + x2)) = 0 (-8x + 4x2 + (-2x * 2x + x2 * 2x)) = 0 (-8x + 4x2 + (-4x2 + 2x3)) = 0 Combine like terms: 4x2 + -4x2 = 0 (-8x + 0 + 2x3) = 0 (-8x + 2x3) = 0 Solving -8x + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-4 + x2) = 0 Factor a difference between two squares. 2x((2 + x)(-2 + x)) = 0 Ignore the factor 2.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 '(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 3
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 = 2Solution
x = {0, -2, 2}
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