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Simplifying (12 + 2x)(16 + 2x) = 672 Multiply (12 + 2x) * (16 + 2x) (12(16 + 2x) + 2x * (16 + 2x)) = 672 ((16 * 12 + 2x * 12) + 2x * (16 + 2x)) = 672 ((192 + 24x) + 2x * (16 + 2x)) = 672 (192 + 24x + (16 * 2x + 2x * 2x)) = 672 (192 + 24x + (32x + 4x2)) = 672 Combine like terms: 24x + 32x = 56x (192 + 56x + 4x2) = 672 Solving 192 + 56x + 4x2 = 672 Solving for variable 'x'. Reorder the terms: 192 + -672 + 56x + 4x2 = 672 + -672 Combine like terms: 192 + -672 = -480 -480 + 56x + 4x2 = 672 + -672 Combine like terms: 672 + -672 = 0 -480 + 56x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-120 + 14x + x2) = 0 Factor a trinomial. 4((-20 + -1x)(6 + -1x)) = 0 Ignore the factor 4.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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-20, 6}
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