u^2-uv-12v^2=0

Solution for u^2-uv-12v^2=0 equation:

Simplifying
u2 + -1uv + -12v2 = 0

Reorder the terms:
-1uv + u2 + -12v2 = 0

Solving
-1uv + u2 + -12v2 = 0

Solving for variable 'u'.

Factor a trinomial.
(u + -4v)(u + 3v) = 0

Subproblem 1
Set the factor '(u + -4v)' equal to zero and attempt to solve:

Simplifying
u + -4v = 0

Solving
u + -4v = 0

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

Add '4v' to each side of the equation.
u + -4v + 4v = 0 + 4v

Combine like terms: -4v + 4v = 0
u + 0 = 0 + 4v
u = 0 + 4v
Remove the zero:
u = 4v

Simplifying
u = 4v
Subproblem 2
Set the factor '(u + 3v)' equal to zero and attempt to solve:

Simplifying
u + 3v = 0

Solving
u + 3v = 0

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

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

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

Simplifying
u = -3v
Solution
u = {4v, -3v}