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Simplifying (12 + -2x)(9 + -2x) = 54 Multiply (12 + -2x) * (9 + -2x) (12(9 + -2x) + -2x * (9 + -2x)) = 54 ((9 * 12 + -2x * 12) + -2x * (9 + -2x)) = 54 ((108 + -24x) + -2x * (9 + -2x)) = 54 (108 + -24x + (9 * -2x + -2x * -2x)) = 54 (108 + -24x + (-18x + 4x2)) = 54 Combine like terms: -24x + -18x = -42x (108 + -42x + 4x2) = 54 Solving 108 + -42x + 4x2 = 54 Solving for variable 'x'. Reorder the terms: 108 + -54 + -42x + 4x2 = 54 + -54 Combine like terms: 108 + -54 = 54 54 + -42x + 4x2 = 54 + -54 Combine like terms: 54 + -54 = 0 54 + -42x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(27 + -21x + 2x2) = 0 Factor a trinomial. 2((3 + -2x)(9 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Subproblem 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 = {1.5, 9}
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