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Simplifying 108 + 3x2 + -3x = 36x + -18 Reorder the terms: 108 + -3x + 3x2 = 36x + -18 Reorder the terms: 108 + -3x + 3x2 = -18 + 36x Solving 108 + -3x + 3x2 = -18 + 36x Solving for variable 'x'. Reorder the terms: 108 + 18 + -3x + -36x + 3x2 = -18 + 36x + 18 + -36x Combine like terms: 108 + 18 = 126 126 + -3x + -36x + 3x2 = -18 + 36x + 18 + -36x Combine like terms: -3x + -36x = -39x 126 + -39x + 3x2 = -18 + 36x + 18 + -36x Reorder the terms: 126 + -39x + 3x2 = -18 + 18 + 36x + -36x Combine like terms: -18 + 18 = 0 126 + -39x + 3x2 = 0 + 36x + -36x 126 + -39x + 3x2 = 36x + -36x Combine like terms: 36x + -36x = 0 126 + -39x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(42 + -13x + x2) = 0 Factor a trinomial. 3((6 + -1x)(7 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {6, 7}
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