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Simplifying 6(3x + -3)(x + 4) = 0 Reorder the terms: 6(-3 + 3x)(x + 4) = 0 Reorder the terms: 6(-3 + 3x)(4 + x) = 0 Multiply (-3 + 3x) * (4 + x) 6(-3(4 + x) + 3x * (4 + x)) = 0 6((4 * -3 + x * -3) + 3x * (4 + x)) = 0 6((-12 + -3x) + 3x * (4 + x)) = 0 6(-12 + -3x + (4 * 3x + x * 3x)) = 0 6(-12 + -3x + (12x + 3x2)) = 0 Combine like terms: -3x + 12x = 9x 6(-12 + 9x + 3x2) = 0 (-12 * 6 + 9x * 6 + 3x2 * 6) = 0 (-72 + 54x + 18x2) = 0 Solving -72 + 54x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '18'. 18(-4 + 3x + x2) = 0 Factor a trinomial. 18((-4 + -1x)(1 + -1x)) = 0 Ignore the factor 18.Subproblem 1
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 = -4Subproblem 2
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 = 1Solution
x = {-4, 1}
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