56v^2-vy-y^2=0

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Solution for 56v^2-vy-y^2=0 equation: 


Simplifying
56v2 + -1vy + -1y2 = 0

Reorder the terms:
-1vy + 56v2 + -1y2 = 0

Solving
-1vy + 56v2 + -1y2 = 0

Solving for variable 'v'.

Factor a trinomial.
(7v + -1y)(8v + y) = 0


Subproblem 1
Set the factor '(7v + -1y)' equal to zero and attempt to solve:

Simplifying
7v + -1y = 0

Solving
7v + -1y = 0

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

Add 'y' to each side of the equation.
7v + -1y + y = 0 + y

Combine like terms: -1y + y = 0
7v + 0 = 0 + y
7v = 0 + y
Remove the zero:
7v = y

Divide each side by '7'.
v = 0.1428571429y

Simplifying
v = 0.1428571429y

Subproblem 2
Set the factor '(8v + y)' equal to zero and attempt to solve:

Simplifying
8v + y = 0

Solving
8v + y = 0

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

Add '-1y' to each side of the equation.
8v + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
8v + 0 = 0 + -1y
8v = 0 + -1y
Remove the zero:
8v = -1y

Divide each side by '8'.
v = -0.125y

Simplifying
v = -0.125y
Solution
v = {0.1428571429y, -0.125y}

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