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Simplifying 12(x + -2)(3x + 1) = 0 Reorder the terms: 12(-2 + x)(3x + 1) = 0 Reorder the terms: 12(-2 + x)(1 + 3x) = 0 Multiply (-2 + x) * (1 + 3x) 12(-2(1 + 3x) + x(1 + 3x)) = 0 12((1 * -2 + 3x * -2) + x(1 + 3x)) = 0 12((-2 + -6x) + x(1 + 3x)) = 0 12(-2 + -6x + (1 * x + 3x * x)) = 0 12(-2 + -6x + (1x + 3x2)) = 0 Combine like terms: -6x + 1x = -5x 12(-2 + -5x + 3x2) = 0 (-2 * 12 + -5x * 12 + 3x2 * 12) = 0 (-24 + -60x + 36x2) = 0 Solving -24 + -60x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(-2 + -5x + 3x2) = 0 Factor a trinomial. 12((-1 + -3x)(2 + -1x)) = 0 Ignore the factor 12.Subproblem 1
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 = -0.3333333333Subproblem 2
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 = 2Solution
x = {-0.3333333333, 2}
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