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Simplifying (3x + 6)(2x + -1) = 0 Reorder the terms: (6 + 3x)(2x + -1) = 0 Reorder the terms: (6 + 3x)(-1 + 2x) = 0 Multiply (6 + 3x) * (-1 + 2x) (6(-1 + 2x) + 3x * (-1 + 2x)) = 0 ((-1 * 6 + 2x * 6) + 3x * (-1 + 2x)) = 0 ((-6 + 12x) + 3x * (-1 + 2x)) = 0 (-6 + 12x + (-1 * 3x + 2x * 3x)) = 0 (-6 + 12x + (-3x + 6x2)) = 0 Combine like terms: 12x + -3x = 9x (-6 + 9x + 6x2) = 0 Solving -6 + 9x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + 3x + 2x2) = 0 Factor a trinomial. 3((-2 + -1x)(1 + -2x)) = 0 Ignore the factor 3.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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