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Simplifying (12 + 2x)(18 + 2x) = 432 Multiply (12 + 2x) * (18 + 2x) (12(18 + 2x) + 2x * (18 + 2x)) = 432 ((18 * 12 + 2x * 12) + 2x * (18 + 2x)) = 432 ((216 + 24x) + 2x * (18 + 2x)) = 432 (216 + 24x + (18 * 2x + 2x * 2x)) = 432 (216 + 24x + (36x + 4x2)) = 432 Combine like terms: 24x + 36x = 60x (216 + 60x + 4x2) = 432 Solving 216 + 60x + 4x2 = 432 Solving for variable 'x'. Reorder the terms: 216 + -432 + 60x + 4x2 = 432 + -432 Combine like terms: 216 + -432 = -216 -216 + 60x + 4x2 = 432 + -432 Combine like terms: 432 + -432 = 0 -216 + 60x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-54 + 15x + x2) = 0 Factor a trinomial. 4((-18 + -1x)(3 + -1x)) = 0 Ignore the factor 4.Subproblem 1
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 = -18Subproblem 2
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 = 3Solution
x = {-18, 3}
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