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Simplifying (18x + -54)(9x + 18) = 0 Reorder the terms: (-54 + 18x)(9x + 18) = 0 Reorder the terms: (-54 + 18x)(18 + 9x) = 0 Multiply (-54 + 18x) * (18 + 9x) (-54(18 + 9x) + 18x * (18 + 9x)) = 0 ((18 * -54 + 9x * -54) + 18x * (18 + 9x)) = 0 ((-972 + -486x) + 18x * (18 + 9x)) = 0 (-972 + -486x + (18 * 18x + 9x * 18x)) = 0 (-972 + -486x + (324x + 162x2)) = 0 Combine like terms: -486x + 324x = -162x (-972 + -162x + 162x2) = 0 Solving -972 + -162x + 162x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '162'. 162(-6 + -1x + x2) = 0 Factor a trinomial. 162((-2 + -1x)(3 + -1x)) = 0 Ignore the factor 162.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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-2, 3}
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