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