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Simplifying 3x2 = 117 + 30x Solving 3x2 = 117 + 30x Solving for variable 'x'. Reorder the terms: -117 + -30x + 3x2 = 117 + 30x + -117 + -30x Reorder the terms: -117 + -30x + 3x2 = 117 + -117 + 30x + -30x Combine like terms: 117 + -117 = 0 -117 + -30x + 3x2 = 0 + 30x + -30x -117 + -30x + 3x2 = 30x + -30x Combine like terms: 30x + -30x = 0 -117 + -30x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-39 + -10x + x2) = 0 Factor a trinomial. 3((-3 + -1x)(13 + -1x)) = 0 Ignore the factor 3.Subproblem 1
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 = -3Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve: Simplifying 13 + -1x = 0 Solving 13 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1x = 0 + -13 -1x = 0 + -13 Combine like terms: 0 + -13 = -13 -1x = -13 Divide each side by '-1'. x = 13 Simplifying x = 13Solution
x = {-3, 13}
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