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Simplifying w2 + 12wg + 32g2 = 0 Reorder the terms: 12gw + 32g2 + w2 = 0 Solving 12gw + 32g2 + w2 = 0 Solving for variable 'g'. Factor a trinomial. (8g + w)(4g + w) = 0Subproblem 1
Set the factor '(8g + w)' equal to zero and attempt to solve: Simplifying 8g + w = 0 Solving 8g + w = 0 Move all terms containing g to the left, all other terms to the right. Add '-1w' to each side of the equation. 8g + w + -1w = 0 + -1w Combine like terms: w + -1w = 0 8g + 0 = 0 + -1w 8g = 0 + -1w Remove the zero: 8g = -1w Divide each side by '8'. g = -0.125w Simplifying g = -0.125wSubproblem 2
Set the factor '(4g + w)' equal to zero and attempt to solve: Simplifying 4g + w = 0 Solving 4g + w = 0 Move all terms containing g to the left, all other terms to the right. Add '-1w' to each side of the equation. 4g + w + -1w = 0 + -1w Combine like terms: w + -1w = 0 4g + 0 = 0 + -1w 4g = 0 + -1w Remove the zero: 4g = -1w Divide each side by '4'. g = -0.25w Simplifying g = -0.25wSolution
g = {-0.125w, -0.25w}
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