u^2+8uv+12v^2=0

Solution for u^2+8uv+12v^2=0 equation:

Simplifying
u2 + 8uv + 12v2 = 0

Reorder the terms:
8uv + u2 + 12v2 = 0

Solving
8uv + u2 + 12v2 = 0

Solving for variable 'u'.

Factor a trinomial.
(u + 2v)(u + 6v) = 0

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

Simplifying
u + 2v = 0

Solving
u + 2v = 0

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

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

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

Simplifying
u = -2v
Subproblem 2
Set the factor '(u + 6v)' equal to zero and attempt to solve:

Simplifying
u + 6v = 0

Solving
u + 6v = 0

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

Add '-6v' to each side of the equation.
u + 6v + -6v = 0 + -6v

Combine like terms: 6v + -6v = 0
u + 0 = 0 + -6v
u = 0 + -6v
Remove the zero:
u = -6v

Simplifying
u = -6v
Solution
u = {-2v, -6v}