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Simplifying (15 + -2x)(18 + -2x) = 108 Multiply (15 + -2x) * (18 + -2x) (15(18 + -2x) + -2x * (18 + -2x)) = 108 ((18 * 15 + -2x * 15) + -2x * (18 + -2x)) = 108 ((270 + -30x) + -2x * (18 + -2x)) = 108 (270 + -30x + (18 * -2x + -2x * -2x)) = 108 (270 + -30x + (-36x + 4x2)) = 108 Combine like terms: -30x + -36x = -66x (270 + -66x + 4x2) = 108 Solving 270 + -66x + 4x2 = 108 Solving for variable 'x'. Reorder the terms: 270 + -108 + -66x + 4x2 = 108 + -108 Combine like terms: 270 + -108 = 162 162 + -66x + 4x2 = 108 + -108 Combine like terms: 108 + -108 = 0 162 + -66x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(81 + -33x + 2x2) = 0 Factor a trinomial. 2((3 + -1x)(27 + -2x)) = 0 Ignore the factor 2.Subproblem 1
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 = 3Subproblem 2
Set the factor '(27 + -2x)' equal to zero and attempt to solve: Simplifying 27 + -2x = 0 Solving 27 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + -2x = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -2x = 0 + -27 -2x = 0 + -27 Combine like terms: 0 + -27 = -27 -2x = -27 Divide each side by '-2'. x = 13.5 Simplifying x = 13.5Solution
x = {3, 13.5}
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