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Simplifying (3x + -12)(4 + 2x) = 0 Reorder the terms: (-12 + 3x)(4 + 2x) = 0 Multiply (-12 + 3x) * (4 + 2x) (-12(4 + 2x) + 3x * (4 + 2x)) = 0 ((4 * -12 + 2x * -12) + 3x * (4 + 2x)) = 0 ((-48 + -24x) + 3x * (4 + 2x)) = 0 (-48 + -24x + (4 * 3x + 2x * 3x)) = 0 (-48 + -24x + (12x + 6x2)) = 0 Combine like terms: -24x + 12x = -12x (-48 + -12x + 6x2) = 0 Solving -48 + -12x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-8 + -2x + x2) = 0 Factor a trinomial. 6((-2 + -1x)(4 + -1x)) = 0 Ignore the factor 6.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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-2, 4}
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