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Simplifying 2(0 + x)(12 + x) = 128 Remove the zero: 2(x)(12 + x) = 128 (12 * 2x + x * 2x) = 128 (24x + 2x2) = 128 Solving 24x + 2x2 = 128 Solving for variable 'x'. Reorder the terms: -128 + 24x + 2x2 = 128 + -128 Combine like terms: 128 + -128 = 0 -128 + 24x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-64 + 12x + x2) = 0 Factor a trinomial. 2((-16 + -1x)(4 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + -1x)' equal to zero and attempt to solve: Simplifying -16 + -1x = 0 Solving -16 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + -1x = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -1x = 0 + 16 -1x = 0 + 16 Combine like terms: 0 + 16 = 16 -1x = 16 Divide each side by '-1'. x = -16 Simplifying x = -16Subproblem 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 = {-16, 4}
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