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Simplifying 18g2 + 27g + -81 = 0 Reorder the terms: -81 + 27g + 18g2 = 0 Solving -81 + 27g + 18g2 = 0 Solving for variable 'g'. Factor out the Greatest Common Factor (GCF), '9'. 9(-9 + 3g + 2g2) = 0 Factor a trinomial. 9((-3 + -1g)(3 + -2g)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-3 + -1g)' equal to zero and attempt to solve: Simplifying -3 + -1g = 0 Solving -3 + -1g = 0 Move all terms containing g to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1g = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1g = 0 + 3 -1g = 0 + 3 Combine like terms: 0 + 3 = 3 -1g = 3 Divide each side by '-1'. g = -3 Simplifying g = -3Subproblem 2
Set the factor '(3 + -2g)' equal to zero and attempt to solve: Simplifying 3 + -2g = 0 Solving 3 + -2g = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2g = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2g = 0 + -3 -2g = 0 + -3 Combine like terms: 0 + -3 = -3 -2g = -3 Divide each side by '-2'. g = 1.5 Simplifying g = 1.5Solution
g = {-3, 1.5}
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