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Simplifying 6g2 + -54g + -132 = 0 Reorder the terms: -132 + -54g + 6g2 = 0 Solving -132 + -54g + 6g2 = 0 Solving for variable 'g'. Factor out the Greatest Common Factor (GCF), '6'. 6(-22 + -9g + g2) = 0 Factor a trinomial. 6((-2 + -1g)(11 + -1g)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-2 + -1g)' equal to zero and attempt to solve: Simplifying -2 + -1g = 0 Solving -2 + -1g = 0 Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1g = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1g = 0 + 2 -1g = 0 + 2 Combine like terms: 0 + 2 = 2 -1g = 2 Divide each side by '-1'. g = -2 Simplifying g = -2Subproblem 2
Set the factor '(11 + -1g)' equal to zero and attempt to solve: Simplifying 11 + -1g = 0 Solving 11 + -1g = 0 Move all terms containing g to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1g = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1g = 0 + -11 -1g = 0 + -11 Combine like terms: 0 + -11 = -11 -1g = -11 Divide each side by '-1'. g = 11 Simplifying g = 11Solution
g = {-2, 11}
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