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Simplifying (6 + 3x)(-6x + 24) = 0 Reorder the terms: (6 + 3x)(24 + -6x) = 0 Multiply (6 + 3x) * (24 + -6x) (6(24 + -6x) + 3x * (24 + -6x)) = 0 ((24 * 6 + -6x * 6) + 3x * (24 + -6x)) = 0 ((144 + -36x) + 3x * (24 + -6x)) = 0 (144 + -36x + (24 * 3x + -6x * 3x)) = 0 (144 + -36x + (72x + -18x2)) = 0 Combine like terms: -36x + 72x = 36x (144 + 36x + -18x2) = 0 Solving 144 + 36x + -18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '18'. 18(8 + 2x + -1x2) = 0 Factor a trinomial. 18((4 + -1x)(2 + x)) = 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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {4, -2}
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