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Simplifying (9x + -2)(6x + 3) = 0 Reorder the terms: (-2 + 9x)(6x + 3) = 0 Reorder the terms: (-2 + 9x)(3 + 6x) = 0 Multiply (-2 + 9x) * (3 + 6x) (-2(3 + 6x) + 9x * (3 + 6x)) = 0 ((3 * -2 + 6x * -2) + 9x * (3 + 6x)) = 0 ((-6 + -12x) + 9x * (3 + 6x)) = 0 (-6 + -12x + (3 * 9x + 6x * 9x)) = 0 (-6 + -12x + (27x + 54x2)) = 0 Combine like terms: -12x + 27x = 15x (-6 + 15x + 54x2) = 0 Solving -6 + 15x + 54x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + 5x + 18x2) = 0 Factor a trinomial. 3((-1 + -2x)(2 + -9x)) = 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 '(2 + -9x)' equal to zero and attempt to solve: Simplifying 2 + -9x = 0 Solving 2 + -9x = 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 + -9x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -9x = 0 + -2 -9x = 0 + -2 Combine like terms: 0 + -2 = -2 -9x = -2 Divide each side by '-9'. x = 0.2222222222 Simplifying x = 0.2222222222Solution
x = {-0.5, 0.2222222222}
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