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Simplifying 75r2 + 90rg + 27g2 = 0 Reorder the terms: 90gr + 27g2 + 75r2 = 0 Solving 90gr + 27g2 + 75r2 = 0 Solving for variable 'g'. Factor out the Greatest Common Factor (GCF), '3'. 3(30gr + 9g2 + 25r2) = 0 Factor a trinomial. 3((3g + 5r)(3g + 5r)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3g + 5r)' equal to zero and attempt to solve: Simplifying 3g + 5r = 0 Solving 3g + 5r = 0 Move all terms containing g to the left, all other terms to the right. Add '-5r' to each side of the equation. 3g + 5r + -5r = 0 + -5r Combine like terms: 5r + -5r = 0 3g + 0 = 0 + -5r 3g = 0 + -5r Remove the zero: 3g = -5r Divide each side by '3'. g = -1.666666667r Simplifying g = -1.666666667rSubproblem 2
Set the factor '(3g + 5r)' equal to zero and attempt to solve: Simplifying 3g + 5r = 0 Solving 3g + 5r = 0 Move all terms containing g to the left, all other terms to the right. Add '-5r' to each side of the equation. 3g + 5r + -5r = 0 + -5r Combine like terms: 5r + -5r = 0 3g + 0 = 0 + -5r 3g = 0 + -5r Remove the zero: 3g = -5r Divide each side by '3'. g = -1.666666667r Simplifying g = -1.666666667rSolution
g = {-1.666666667r, -1.666666667r}
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