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Simplifying (2x + -3)(3x + -9) = 0 Reorder the terms: (-3 + 2x)(3x + -9) = 0 Reorder the terms: (-3 + 2x)(-9 + 3x) = 0 Multiply (-3 + 2x) * (-9 + 3x) (-3(-9 + 3x) + 2x * (-9 + 3x)) = 0 ((-9 * -3 + 3x * -3) + 2x * (-9 + 3x)) = 0 ((27 + -9x) + 2x * (-9 + 3x)) = 0 (27 + -9x + (-9 * 2x + 3x * 2x)) = 0 (27 + -9x + (-18x + 6x2)) = 0 Combine like terms: -9x + -18x = -27x (27 + -27x + 6x2) = 0 Solving 27 + -27x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(9 + -9x + 2x2) = 0 Factor a trinomial. 3((3 + -2x)(3 + -1x)) = 0 Ignore the factor 3.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 '(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 = 3Solution
x = {1.5, 3}
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