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Simplifying (3x + -1)(2x + 6) = 0 Reorder the terms: (-1 + 3x)(2x + 6) = 0 Reorder the terms: (-1 + 3x)(6 + 2x) = 0 Multiply (-1 + 3x) * (6 + 2x) (-1(6 + 2x) + 3x * (6 + 2x)) = 0 ((6 * -1 + 2x * -1) + 3x * (6 + 2x)) = 0 ((-6 + -2x) + 3x * (6 + 2x)) = 0 (-6 + -2x + (6 * 3x + 2x * 3x)) = 0 (-6 + -2x + (18x + 6x2)) = 0 Combine like terms: -2x + 18x = 16x (-6 + 16x + 6x2) = 0 Solving -6 + 16x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 8x + 3x2) = 0 Factor a trinomial. 2((-3 + -1x)(1 + -3x)) = 0 Ignore the factor 2.Subproblem 1
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 = -3Subproblem 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 = {-3, 0.3333333333}
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