0=v^2-3vy-70y^2

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Solution for 0=v^2-3vy-70y^2 equation: 


Simplifying
0 = v2 + -3vy + -70y2

Reorder the terms:
0 = -3vy + v2 + -70y2

Solving
0 = -3vy + v2 + -70y2

Solving for variable 'v'.
Remove the zero:
3vy + -1v2 + 70y2 = -3vy + v2 + -70y2 + 3vy + -1v2 + 70y2

Reorder the terms:
3vy + -1v2 + 70y2 = -3vy + 3vy + v2 + -1v2 + -70y2 + 70y2

Combine like terms: -3vy + 3vy = 0
3vy + -1v2 + 70y2 = 0 + v2 + -1v2 + -70y2 + 70y2
3vy + -1v2 + 70y2 = v2 + -1v2 + -70y2 + 70y2

Combine like terms: v2 + -1v2 = 0
3vy + -1v2 + 70y2 = 0 + -70y2 + 70y2
3vy + -1v2 + 70y2 = -70y2 + 70y2

Combine like terms: -70y2 + 70y2 = 0
3vy + -1v2 + 70y2 = 0

Factor a trinomial.
(-1v + -7y)(v + -10y) = 0


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

Simplifying
-1v + -7y = 0

Solving
-1v + -7y = 0

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

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

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

Divide each side by '-1'.
v = -7y

Simplifying
v = -7y

Subproblem 2
Set the factor '(v + -10y)' equal to zero and attempt to solve:

Simplifying
v + -10y = 0

Solving
v + -10y = 0

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

Add '10y' to each side of the equation.
v + -10y + 10y = 0 + 10y

Combine like terms: -10y + 10y = 0
v + 0 = 0 + 10y
v = 0 + 10y
Remove the zero:
v = 10y

Simplifying
v = 10y
Solution
v = {-7y, 10y}

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