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Simplifying (3x + -9)(2x + 1) = 0 Reorder the terms: (-9 + 3x)(2x + 1) = 0 Reorder the terms: (-9 + 3x)(1 + 2x) = 0 Multiply (-9 + 3x) * (1 + 2x) (-9(1 + 2x) + 3x * (1 + 2x)) = 0 ((1 * -9 + 2x * -9) + 3x * (1 + 2x)) = 0 ((-9 + -18x) + 3x * (1 + 2x)) = 0 (-9 + -18x + (1 * 3x + 2x * 3x)) = 0 (-9 + -18x + (3x + 6x2)) = 0 Combine like terms: -18x + 3x = -15x (-9 + -15x + 6x2) = 0 Solving -9 + -15x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + -5x + 2x2) = 0 Factor a trinomial. 3((-1 + -2x)(3 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 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 = {-0.5, 3}
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