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Simplifying (0.5x)(2x + -6) = 108 Remove parenthesis around (0.5x) 0.5x(2x + -6) = 108 Reorder the terms: 0.5x(-6 + 2x) = 108 (-6 * 0.5x + 2x * 0.5x) = 108 (-3x + 1x2) = 108 Solving -3x + 1x2 = 108 Solving for variable 'x'. Reorder the terms: -108 + -3x + 1x2 = 108 + -108 Combine like terms: 108 + -108 = 0 -108 + -3x + 1x2 = 0 Factor a trinomial. (-9 + -1x)(12 + -1x) = 0Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12Solution
x = {-9, 12}
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