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Simplifying (12 + -2x)(8 + -2x) = 60 Multiply (12 + -2x) * (8 + -2x) (12(8 + -2x) + -2x * (8 + -2x)) = 60 ((8 * 12 + -2x * 12) + -2x * (8 + -2x)) = 60 ((96 + -24x) + -2x * (8 + -2x)) = 60 (96 + -24x + (8 * -2x + -2x * -2x)) = 60 (96 + -24x + (-16x + 4x2)) = 60 Combine like terms: -24x + -16x = -40x (96 + -40x + 4x2) = 60 Solving 96 + -40x + 4x2 = 60 Solving for variable 'x'. Reorder the terms: 96 + -60 + -40x + 4x2 = 60 + -60 Combine like terms: 96 + -60 = 36 36 + -40x + 4x2 = 60 + -60 Combine like terms: 60 + -60 = 0 36 + -40x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(9 + -10x + x2) = 0 Factor a trinomial. 4((1 + -1x)(9 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {1, 9}
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