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Simplifying (2x + -4)(3x + -9) = 0 Reorder the terms: (-4 + 2x)(3x + -9) = 0 Reorder the terms: (-4 + 2x)(-9 + 3x) = 0 Multiply (-4 + 2x) * (-9 + 3x) (-4(-9 + 3x) + 2x * (-9 + 3x)) = 0 ((-9 * -4 + 3x * -4) + 2x * (-9 + 3x)) = 0 ((36 + -12x) + 2x * (-9 + 3x)) = 0 (36 + -12x + (-9 * 2x + 3x * 2x)) = 0 (36 + -12x + (-18x + 6x2)) = 0 Combine like terms: -12x + -18x = -30x (36 + -30x + 6x2) = 0 Solving 36 + -30x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(6 + -5x + x2) = 0 Factor a trinomial. 6((2 + -1x)(3 + -1x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 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 = {2, 3}
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