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Simplifying (3x + -6)(6x + 9) = 0 Reorder the terms: (-6 + 3x)(6x + 9) = 0 Reorder the terms: (-6 + 3x)(9 + 6x) = 0 Multiply (-6 + 3x) * (9 + 6x) (-6(9 + 6x) + 3x * (9 + 6x)) = 0 ((9 * -6 + 6x * -6) + 3x * (9 + 6x)) = 0 ((-54 + -36x) + 3x * (9 + 6x)) = 0 (-54 + -36x + (9 * 3x + 6x * 3x)) = 0 (-54 + -36x + (27x + 18x2)) = 0 Combine like terms: -36x + 27x = -9x (-54 + -9x + 18x2) = 0 Solving -54 + -9x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(-6 + -1x + 2x2) = 0 Factor a trinomial. 9((-3 + -2x)(2 + -1x)) = 0 Ignore the factor 9.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 '(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 = 2Solution
x = {-1.5, 2}
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