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Simplifying 108 = (15 + -1x)(12 + -1x) Multiply (15 + -1x) * (12 + -1x) 108 = (15(12 + -1x) + -1x * (12 + -1x)) 108 = ((12 * 15 + -1x * 15) + -1x * (12 + -1x)) 108 = ((180 + -15x) + -1x * (12 + -1x)) 108 = (180 + -15x + (12 * -1x + -1x * -1x)) 108 = (180 + -15x + (-12x + 1x2)) Combine like terms: -15x + -12x = -27x 108 = (180 + -27x + 1x2) Solving 108 = 180 + -27x + 1x2 Solving for variable 'x'. Combine like terms: 108 + -180 = -72 -72 + 27x + -1x2 = 180 + -27x + 1x2 + -180 + 27x + -1x2 Reorder the terms: -72 + 27x + -1x2 = 180 + -180 + -27x + 27x + 1x2 + -1x2 Combine like terms: 180 + -180 = 0 -72 + 27x + -1x2 = 0 + -27x + 27x + 1x2 + -1x2 -72 + 27x + -1x2 = -27x + 27x + 1x2 + -1x2 Combine like terms: -27x + 27x = 0 -72 + 27x + -1x2 = 0 + 1x2 + -1x2 -72 + 27x + -1x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 -72 + 27x + -1x2 = 0 Factor a trinomial. (-24 + x)(3 + -1x) = 0Subproblem 1
Set the factor '(-24 + x)' equal to zero and attempt to solve: Simplifying -24 + x = 0 Solving -24 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = 0 + 24 Combine like terms: -24 + 24 = 0 0 + x = 0 + 24 x = 0 + 24 Combine like terms: 0 + 24 = 24 x = 24 Simplifying x = 24Subproblem 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 = {24, 3}
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