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Simplifying (4x + 12)(8x + -8) = 0 Reorder the terms: (12 + 4x)(8x + -8) = 0 Reorder the terms: (12 + 4x)(-8 + 8x) = 0 Multiply (12 + 4x) * (-8 + 8x) (12(-8 + 8x) + 4x * (-8 + 8x)) = 0 ((-8 * 12 + 8x * 12) + 4x * (-8 + 8x)) = 0 ((-96 + 96x) + 4x * (-8 + 8x)) = 0 (-96 + 96x + (-8 * 4x + 8x * 4x)) = 0 (-96 + 96x + (-32x + 32x2)) = 0 Combine like terms: 96x + -32x = 64x (-96 + 64x + 32x2) = 0 Solving -96 + 64x + 32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '32'. 32(-3 + 2x + x2) = 0 Factor a trinomial. 32((-3 + -1x)(1 + -1x)) = 0 Ignore the factor 32.Subproblem 1
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 = -3Subproblem 2
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 = 1Solution
x = {-3, 1}
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