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Simplifying (3x + 6)(6x + -3) = 0 Reorder the terms: (6 + 3x)(6x + -3) = 0 Reorder the terms: (6 + 3x)(-3 + 6x) = 0 Multiply (6 + 3x) * (-3 + 6x) (6(-3 + 6x) + 3x * (-3 + 6x)) = 0 ((-3 * 6 + 6x * 6) + 3x * (-3 + 6x)) = 0 ((-18 + 36x) + 3x * (-3 + 6x)) = 0 (-18 + 36x + (-3 * 3x + 6x * 3x)) = 0 (-18 + 36x + (-9x + 18x2)) = 0 Combine like terms: 36x + -9x = 27x (-18 + 27x + 18x2) = 0 Solving -18 + 27x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(-2 + 3x + 2x2) = 0 Factor a trinomial. 9((-2 + -1x)(1 + -2x)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 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 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
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 = 0.5Solution
x = {-2, 0.5}
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