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Simplifying (9x + -3)(6x + 3) = 0 Reorder the terms: (-3 + 9x)(6x + 3) = 0 Reorder the terms: (-3 + 9x)(3 + 6x) = 0 Multiply (-3 + 9x) * (3 + 6x) (-3(3 + 6x) + 9x * (3 + 6x)) = 0 ((3 * -3 + 6x * -3) + 9x * (3 + 6x)) = 0 ((-9 + -18x) + 9x * (3 + 6x)) = 0 (-9 + -18x + (3 * 9x + 6x * 9x)) = 0 (-9 + -18x + (27x + 54x2)) = 0 Combine like terms: -18x + 27x = 9x (-9 + 9x + 54x2) = 0 Solving -9 + 9x + 54x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(-1 + x + 6x2) = 0 Factor a trinomial. 9((-1 + -2x)(1 + -3x)) = 0 Ignore the factor 9.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 '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {-0.5, 0.3333333333}
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