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Simplifying 75w2 + 90wg + 27g2 = 0 Reorder the terms: 90gw + 27g2 + 75w2 = 0 Solving 90gw + 27g2 + 75w2 = 0 Solving for variable 'g'. Factor out the Greatest Common Factor (GCF), '3'. 3(30gw + 9g2 + 25w2) = 0 Factor a trinomial. 3((3g + 5w)(3g + 5w)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3g + 5w)' equal to zero and attempt to solve: Simplifying 3g + 5w = 0 Solving 3g + 5w = 0 Move all terms containing g to the left, all other terms to the right. Add '-5w' to each side of the equation. 3g + 5w + -5w = 0 + -5w Combine like terms: 5w + -5w = 0 3g + 0 = 0 + -5w 3g = 0 + -5w Remove the zero: 3g = -5w Divide each side by '3'. g = -1.666666667w Simplifying g = -1.666666667wSubproblem 2
Set the factor '(3g + 5w)' equal to zero and attempt to solve: Simplifying 3g + 5w = 0 Solving 3g + 5w = 0 Move all terms containing g to the left, all other terms to the right. Add '-5w' to each side of the equation. 3g + 5w + -5w = 0 + -5w Combine like terms: 5w + -5w = 0 3g + 0 = 0 + -5w 3g = 0 + -5w Remove the zero: 3g = -5w Divide each side by '3'. g = -1.666666667w Simplifying g = -1.666666667wSolution
g = {-1.666666667w, -1.666666667w}
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