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Simplifying w2 + 13wg + 42g2 = 0 Reorder the terms: 13gw + 42g2 + w2 = 0 Solving 13gw + 42g2 + w2 = 0 Solving for variable 'g'. Factor a trinomial. (7g + w)(6g + w) = 0Subproblem 1
Set the factor '(7g + w)' equal to zero and attempt to solve: Simplifying 7g + w = 0 Solving 7g + w = 0 Move all terms containing g to the left, all other terms to the right. Add '-1w' to each side of the equation. 7g + w + -1w = 0 + -1w Combine like terms: w + -1w = 0 7g + 0 = 0 + -1w 7g = 0 + -1w Remove the zero: 7g = -1w Divide each side by '7'. g = -0.1428571429w Simplifying g = -0.1428571429wSubproblem 2
Set the factor '(6g + w)' equal to zero and attempt to solve: Simplifying 6g + w = 0 Solving 6g + w = 0 Move all terms containing g to the left, all other terms to the right. Add '-1w' to each side of the equation. 6g + w + -1w = 0 + -1w Combine like terms: w + -1w = 0 6g + 0 = 0 + -1w 6g = 0 + -1w Remove the zero: 6g = -1w Divide each side by '6'. g = -0.1666666667w Simplifying g = -0.1666666667wSolution
g = {-0.1428571429w, -0.1666666667w}
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