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Simplifying 3(x + -4)(2x + 2) = 0 Reorder the terms: 3(-4 + x)(2x + 2) = 0 Reorder the terms: 3(-4 + x)(2 + 2x) = 0 Multiply (-4 + x) * (2 + 2x) 3(-4(2 + 2x) + x(2 + 2x)) = 0 3((2 * -4 + 2x * -4) + x(2 + 2x)) = 0 3((-8 + -8x) + x(2 + 2x)) = 0 3(-8 + -8x + (2 * x + 2x * x)) = 0 3(-8 + -8x + (2x + 2x2)) = 0 Combine like terms: -8x + 2x = -6x 3(-8 + -6x + 2x2) = 0 (-8 * 3 + -6x * 3 + 2x2 * 3) = 0 (-24 + -18x + 6x2) = 0 Solving -24 + -18x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-4 + -3x + x2) = 0 Factor a trinomial. 6((-1 + -1x)(4 + -1x)) = 0 Ignore the factor 6.Subproblem 1
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 = -1Subproblem 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 = {-1, 4}
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