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Simplifying (2x + -6)(3x + 6) = 0 Reorder the terms: (-6 + 2x)(3x + 6) = 0 Reorder the terms: (-6 + 2x)(6 + 3x) = 0 Multiply (-6 + 2x) * (6 + 3x) (-6(6 + 3x) + 2x * (6 + 3x)) = 0 ((6 * -6 + 3x * -6) + 2x * (6 + 3x)) = 0 ((-36 + -18x) + 2x * (6 + 3x)) = 0 (-36 + -18x + (6 * 2x + 3x * 2x)) = 0 (-36 + -18x + (12x + 6x2)) = 0 Combine like terms: -18x + 12x = -6x (-36 + -6x + 6x2) = 0 Solving -36 + -6x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-6 + -1x + 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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