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Simplifying (6x + -9)(3x + 3) = 0 Reorder the terms: (-9 + 6x)(3x + 3) = 0 Reorder the terms: (-9 + 6x)(3 + 3x) = 0 Multiply (-9 + 6x) * (3 + 3x) (-9(3 + 3x) + 6x * (3 + 3x)) = 0 ((3 * -9 + 3x * -9) + 6x * (3 + 3x)) = 0 ((-27 + -27x) + 6x * (3 + 3x)) = 0 (-27 + -27x + (3 * 6x + 3x * 6x)) = 0 (-27 + -27x + (18x + 18x2)) = 0 Combine like terms: -27x + 18x = -9x (-27 + -9x + 18x2) = 0 Solving -27 + -9x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(-3 + -1x + 2x2) = 0 Factor a trinomial. 9((-1 + -1x)(3 + -2x)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
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 = 1.5Solution
x = {-1, 1.5}
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