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Simplifying (12 + -24x)(9 + 5x) = 0 Multiply (12 + -24x) * (9 + 5x) (12(9 + 5x) + -24x * (9 + 5x)) = 0 ((9 * 12 + 5x * 12) + -24x * (9 + 5x)) = 0 ((108 + 60x) + -24x * (9 + 5x)) = 0 (108 + 60x + (9 * -24x + 5x * -24x)) = 0 (108 + 60x + (-216x + -120x2)) = 0 Combine like terms: 60x + -216x = -156x (108 + -156x + -120x2) = 0 Solving 108 + -156x + -120x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(9 + -13x + -10x2) = 0 Factor a trinomial. 12((1 + -2x)(9 + 5x)) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Subproblem 2
Set the factor '(9 + 5x)' equal to zero and attempt to solve: Simplifying 9 + 5x = 0 Solving 9 + 5x = 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 + 5x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 5x = 0 + -9 5x = 0 + -9 Combine like terms: 0 + -9 = -9 5x = -9 Divide each side by '5'. x = -1.8 Simplifying x = -1.8Solution
x = {0.5, -1.8}
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