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Simplifying (4x + -6)(5x + -9) = 0 Reorder the terms: (-6 + 4x)(5x + -9) = 0 Reorder the terms: (-6 + 4x)(-9 + 5x) = 0 Multiply (-6 + 4x) * (-9 + 5x) (-6(-9 + 5x) + 4x * (-9 + 5x)) = 0 ((-9 * -6 + 5x * -6) + 4x * (-9 + 5x)) = 0 ((54 + -30x) + 4x * (-9 + 5x)) = 0 (54 + -30x + (-9 * 4x + 5x * 4x)) = 0 (54 + -30x + (-36x + 20x2)) = 0 Combine like terms: -30x + -36x = -66x (54 + -66x + 20x2) = 0 Solving 54 + -66x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(27 + -33x + 10x2) = 0 Factor a trinomial. 2((3 + -2x)(9 + -5x)) = 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 + -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 = {1.5, 1.8}
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