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Simplifying 32(x + -2) + 8x(x + -2) = 0 Reorder the terms: 32(-2 + x) + 8x(x + -2) = 0 (-2 * 32 + x * 32) + 8x(x + -2) = 0 (-64 + 32x) + 8x(x + -2) = 0 Reorder the terms: -64 + 32x + 8x(-2 + x) = 0 -64 + 32x + (-2 * 8x + x * 8x) = 0 -64 + 32x + (-16x + 8x2) = 0 Combine like terms: 32x + -16x = 16x -64 + 16x + 8x2 = 0 Solving -64 + 16x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(-8 + 2x + x2) = 0 Factor a trinomial. 8((-4 + -1x)(2 + -1x)) = 0 Ignore the factor 8.Subproblem 1
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 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 = 2Solution
x = {-4, 2}
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