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Simplifying (2x + 6)(4x + -16) = 0 Reorder the terms: (6 + 2x)(4x + -16) = 0 Reorder the terms: (6 + 2x)(-16 + 4x) = 0 Multiply (6 + 2x) * (-16 + 4x) (6(-16 + 4x) + 2x * (-16 + 4x)) = 0 ((-16 * 6 + 4x * 6) + 2x * (-16 + 4x)) = 0 ((-96 + 24x) + 2x * (-16 + 4x)) = 0 (-96 + 24x + (-16 * 2x + 4x * 2x)) = 0 (-96 + 24x + (-32x + 8x2)) = 0 Combine like terms: 24x + -32x = -8x (-96 + -8x + 8x2) = 0 Solving -96 + -8x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(-12 + -1x + x2) = 0 Factor a trinomial. 8((-3 + -1x)(4 + -1x)) = 0 Ignore the factor 8.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 '(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 = 4Solution
x = {-3, 4}
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