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Simplifying (12x + -4)(3x + 6) = 0 Reorder the terms: (-4 + 12x)(3x + 6) = 0 Reorder the terms: (-4 + 12x)(6 + 3x) = 0 Multiply (-4 + 12x) * (6 + 3x) (-4(6 + 3x) + 12x * (6 + 3x)) = 0 ((6 * -4 + 3x * -4) + 12x * (6 + 3x)) = 0 ((-24 + -12x) + 12x * (6 + 3x)) = 0 (-24 + -12x + (6 * 12x + 3x * 12x)) = 0 (-24 + -12x + (72x + 36x2)) = 0 Combine like terms: -12x + 72x = 60x (-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((-2 + -1x)(1 + -3x)) = 0 Ignore the factor 12.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 + -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 = {-2, 0.3333333333}
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