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Simplifying 18r2 + 24rg + 8g2 = 0 Reorder the terms: 24gr + 8g2 + 18r2 = 0 Solving 24gr + 8g2 + 18r2 = 0 Solving for variable 'g'. Factor out the Greatest Common Factor (GCF), '2'. 2(12gr + 4g2 + 9r2) = 0 Factor a trinomial. 2((2g + 3r)(2g + 3r)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2g + 3r)' equal to zero and attempt to solve: Simplifying 2g + 3r = 0 Solving 2g + 3r = 0 Move all terms containing g to the left, all other terms to the right. Add '-3r' to each side of the equation. 2g + 3r + -3r = 0 + -3r Combine like terms: 3r + -3r = 0 2g + 0 = 0 + -3r 2g = 0 + -3r Remove the zero: 2g = -3r Divide each side by '2'. g = -1.5r Simplifying g = -1.5rSubproblem 2
Set the factor '(2g + 3r)' equal to zero and attempt to solve: Simplifying 2g + 3r = 0 Solving 2g + 3r = 0 Move all terms containing g to the left, all other terms to the right. Add '-3r' to each side of the equation. 2g + 3r + -3r = 0 + -3r Combine like terms: 3r + -3r = 0 2g + 0 = 0 + -3r 2g = 0 + -3r Remove the zero: 2g = -3r Divide each side by '2'. g = -1.5r Simplifying g = -1.5rSolution
g = {-1.5r, -1.5r}
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