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Simplifying 9w2 + 12wg + 4g2 = 0 Reorder the terms: 12gw + 4g2 + 9w2 = 0 Solving 12gw + 4g2 + 9w2 = 0 Solving for variable 'g'. Factor a trinomial. (2g + 3w)(2g + 3w) = 0Subproblem 1
Set the factor '(2g + 3w)' equal to zero and attempt to solve: Simplifying 2g + 3w = 0 Solving 2g + 3w = 0 Move all terms containing g to the left, all other terms to the right. Add '-3w' to each side of the equation. 2g + 3w + -3w = 0 + -3w Combine like terms: 3w + -3w = 0 2g + 0 = 0 + -3w 2g = 0 + -3w Remove the zero: 2g = -3w Divide each side by '2'. g = -1.5w Simplifying g = -1.5wSubproblem 2
Set the factor '(2g + 3w)' equal to zero and attempt to solve: Simplifying 2g + 3w = 0 Solving 2g + 3w = 0 Move all terms containing g to the left, all other terms to the right. Add '-3w' to each side of the equation. 2g + 3w + -3w = 0 + -3w Combine like terms: 3w + -3w = 0 2g + 0 = 0 + -3w 2g = 0 + -3w Remove the zero: 2g = -3w Divide each side by '2'. g = -1.5w Simplifying g = -1.5wSolution
g = {-1.5w, -1.5w}
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