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Simplifying (9x + -6)(3x + 9) = 0 Reorder the terms: (-6 + 9x)(3x + 9) = 0 Reorder the terms: (-6 + 9x)(9 + 3x) = 0 Multiply (-6 + 9x) * (9 + 3x) (-6(9 + 3x) + 9x * (9 + 3x)) = 0 ((9 * -6 + 3x * -6) + 9x * (9 + 3x)) = 0 ((-54 + -18x) + 9x * (9 + 3x)) = 0 (-54 + -18x + (9 * 9x + 3x * 9x)) = 0 (-54 + -18x + (81x + 27x2)) = 0 Combine like terms: -18x + 81x = 63x (-54 + 63x + 27x2) = 0 Solving -54 + 63x + 27x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(-6 + 7x + 3x2) = 0 Factor a trinomial. 9((-3 + -1x)(2 + -3x)) = 0 Ignore the factor 9.Subproblem 1
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 = -3Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 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 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {-3, 0.6666666667}
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