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Simplifying 42v2 + 17vw + -15w2 = 0 Reorder the terms: 17vw + 42v2 + -15w2 = 0 Solving 17vw + 42v2 + -15w2 = 0 Solving for variable 'v'. Factor a trinomial. (7v + -3w)(6v + 5w) = 0Subproblem 1
Set the factor '(7v + -3w)' equal to zero and attempt to solve: Simplifying 7v + -3w = 0 Solving 7v + -3w = 0 Move all terms containing v to the left, all other terms to the right. Add '3w' to each side of the equation. 7v + -3w + 3w = 0 + 3w Combine like terms: -3w + 3w = 0 7v + 0 = 0 + 3w 7v = 0 + 3w Remove the zero: 7v = 3w Divide each side by '7'. v = 0.4285714286w Simplifying v = 0.4285714286wSubproblem 2
Set the factor '(6v + 5w)' equal to zero and attempt to solve: Simplifying 6v + 5w = 0 Solving 6v + 5w = 0 Move all terms containing v to the left, all other terms to the right. Add '-5w' to each side of the equation. 6v + 5w + -5w = 0 + -5w Combine like terms: 5w + -5w = 0 6v + 0 = 0 + -5w 6v = 0 + -5w Remove the zero: 6v = -5w Divide each side by '6'. v = -0.8333333333w Simplifying v = -0.8333333333wSolution
v = {0.4285714286w, -0.8333333333w}
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