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Simplifying 12r2 + 36rg + 27g2 = 0 Reorder the terms: 36gr + 27g2 + 12r2 = 0 Solving 36gr + 27g2 + 12r2 = 0 Solving for variable 'g'. Factor out the Greatest Common Factor (GCF), '3'. 3(12gr + 9g2 + 4r2) = 0 Factor a trinomial. 3((3g + 2r)(3g + 2r)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3g + 2r)' equal to zero and attempt to solve: Simplifying 3g + 2r = 0 Solving 3g + 2r = 0 Move all terms containing g to the left, all other terms to the right. Add '-2r' to each side of the equation. 3g + 2r + -2r = 0 + -2r Combine like terms: 2r + -2r = 0 3g + 0 = 0 + -2r 3g = 0 + -2r Remove the zero: 3g = -2r Divide each side by '3'. g = -0.6666666667r Simplifying g = -0.6666666667rSubproblem 2
Set the factor '(3g + 2r)' equal to zero and attempt to solve: Simplifying 3g + 2r = 0 Solving 3g + 2r = 0 Move all terms containing g to the left, all other terms to the right. Add '-2r' to each side of the equation. 3g + 2r + -2r = 0 + -2r Combine like terms: 2r + -2r = 0 3g + 0 = 0 + -2r 3g = 0 + -2r Remove the zero: 3g = -2r Divide each side by '3'. g = -0.6666666667r Simplifying g = -0.6666666667rSolution
g = {-0.6666666667r, -0.6666666667r}
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