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Simplifying 12(x + -2)(5x + 3) = 0 Reorder the terms: 12(-2 + x)(5x + 3) = 0 Reorder the terms: 12(-2 + x)(3 + 5x) = 0 Multiply (-2 + x) * (3 + 5x) 12(-2(3 + 5x) + x(3 + 5x)) = 0 12((3 * -2 + 5x * -2) + x(3 + 5x)) = 0 12((-6 + -10x) + x(3 + 5x)) = 0 12(-6 + -10x + (3 * x + 5x * x)) = 0 12(-6 + -10x + (3x + 5x2)) = 0 Combine like terms: -10x + 3x = -7x 12(-6 + -7x + 5x2) = 0 (-6 * 12 + -7x * 12 + 5x2 * 12) = 0 (-72 + -84x + 60x2) = 0 Solving -72 + -84x + 60x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(-6 + -7x + 5x2) = 0 Factor a trinomial. 12((-3 + -5x)(2 + -1x)) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-3 + -5x)' equal to zero and attempt to solve: Simplifying -3 + -5x = 0 Solving -3 + -5x = 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 + -5x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5x = 0 + 3 -5x = 0 + 3 Combine like terms: 0 + 3 = 3 -5x = 3 Divide each side by '-5'. x = -0.6 Simplifying x = -0.6Subproblem 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 = {-0.6, 2}
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