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Simplifying 32x(x + 2) = 11520 Reorder the terms: 32x(2 + x) = 11520 (2 * 32x + x * 32x) = 11520 (64x + 32x2) = 11520 Solving 64x + 32x2 = 11520 Solving for variable 'x'. Reorder the terms: -11520 + 64x + 32x2 = 11520 + -11520 Combine like terms: 11520 + -11520 = 0 -11520 + 64x + 32x2 = 0 Factor out the Greatest Common Factor (GCF), '32'. 32(-360 + 2x + x2) = 0 Factor a trinomial. 32((-20 + -1x)(18 + -1x)) = 0 Ignore the factor 32.Subproblem 1
Set the factor '(-20 + -1x)' equal to zero and attempt to solve: Simplifying -20 + -1x = 0 Solving -20 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + -1x = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -1x = 0 + 20 -1x = 0 + 20 Combine like terms: 0 + 20 = 20 -1x = 20 Divide each side by '-1'. x = -20 Simplifying x = -20Subproblem 2
Set the factor '(18 + -1x)' equal to zero and attempt to solve: Simplifying 18 + -1x = 0 Solving 18 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + -1x = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -1x = 0 + -18 -1x = 0 + -18 Combine like terms: 0 + -18 = -18 -1x = -18 Divide each side by '-1'. x = 18 Simplifying x = 18Solution
x = {-20, 18}
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