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Simplifying 0 = 6x2 + 6x + -120 Reorder the terms: 0 = -120 + 6x + 6x2 Solving 0 = -120 + 6x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 120 = 120 120 + -6x + -6x2 = -120 + 6x + 6x2 + 120 + -6x + -6x2 Reorder the terms: 120 + -6x + -6x2 = -120 + 120 + 6x + -6x + 6x2 + -6x2 Combine like terms: -120 + 120 = 0 120 + -6x + -6x2 = 0 + 6x + -6x + 6x2 + -6x2 120 + -6x + -6x2 = 6x + -6x + 6x2 + -6x2 Combine like terms: 6x + -6x = 0 120 + -6x + -6x2 = 0 + 6x2 + -6x2 120 + -6x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 120 + -6x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(20 + -1x + -1x2) = 0 Factor a trinomial. 6((4 + -1x)(5 + x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {4, -5}
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