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Simplifying 27g2 + 90g + 75 = 0 Reorder the terms: 75 + 90g + 27g2 = 0 Solving 75 + 90g + 27g2 = 0 Solving for variable 'g'. Factor out the Greatest Common Factor (GCF), '3'. 3(25 + 30g + 9g2) = 0 Factor a trinomial. 3((5 + 3g)(5 + 3g)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + 3g)' equal to zero and attempt to solve: Simplifying 5 + 3g = 0 Solving 5 + 3g = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3g = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3g = 0 + -5 3g = 0 + -5 Combine like terms: 0 + -5 = -5 3g = -5 Divide each side by '3'. g = -1.666666667 Simplifying g = -1.666666667Subproblem 2
Set the factor '(5 + 3g)' equal to zero and attempt to solve: Simplifying 5 + 3g = 0 Solving 5 + 3g = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3g = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3g = 0 + -5 3g = 0 + -5 Combine like terms: 0 + -5 = -5 3g = -5 Divide each side by '3'. g = -1.666666667 Simplifying g = -1.666666667Solution
g = {-1.666666667, -1.666666667}
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