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Simplifying 2x^{2}+ 14x = 120 Reorder the terms: 14x + 2x^{2}= 120 Solving 14x + 2x^{2}= 120 Solving for variable 'x'. Reorder the terms: -120 + 14x + 2x^{2}= 120 + -120 Combine like terms: 120 + -120 = 0 -120 + 14x + 2x^{2}= 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-60 + 7x + x^{2}) = 0 Factor a trinomial. 2((-12 + -1x)(5 + -1x)) = 0 Ignore the factor 2.## Subproblem 1

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 = -12## Subproblem 2

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5## Solution

x = {-12, 5}

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