56v^2-78vw-9w^2=0

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Solution for 56v^2-78vw-9w^2=0 equation: 


Simplifying
56v2 + -78vw + -9w2 = 0

Reorder the terms:
-78vw + 56v2 + -9w2 = 0

Solving
-78vw + 56v2 + -9w2 = 0

Solving for variable 'v'.

Factor a trinomial.
(2v + -3w)(28v + 3w) = 0


Subproblem 1
Set the factor '(2v + -3w)' equal to zero and attempt to solve:

Simplifying
2v + -3w = 0

Solving
2v + -3w = 0

Move all terms containing v to the left, all other terms to the right.

Add '3w' to each side of the equation.
2v + -3w + 3w = 0 + 3w

Combine like terms: -3w + 3w = 0
2v + 0 = 0 + 3w
2v = 0 + 3w
Remove the zero:
2v = 3w

Divide each side by '2'.
v = 1.5w

Simplifying
v = 1.5w

Subproblem 2
Set the factor '(28v + 3w)' equal to zero and attempt to solve:

Simplifying
28v + 3w = 0

Solving
28v + 3w = 0

Move all terms containing v to the left, all other terms to the right.

Add '-3w' to each side of the equation.
28v + 3w + -3w = 0 + -3w

Combine like terms: 3w + -3w = 0
28v + 0 = 0 + -3w
28v = 0 + -3w
Remove the zero:
28v = -3w

Divide each side by '28'.
v = -0.1071428571w

Simplifying
v = -0.1071428571w
Solution
v = {1.5w, -0.1071428571w}

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