42v^2+17vw-15w^2=0

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Solution for 42v^2+17vw-15w^2=0 equation: 


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) = 0


Subproblem 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 = 0.4285714286w

Subproblem 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 = -0.8333333333w
Solution
v = {0.4285714286w, -0.8333333333w}

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