U^2+3V^2-4UV=0

Solution for U^2+3V^2-4UV=0 equation:

Simplifying
U2 + 3V2 + -4UV = 0

Reorder the terms:
-4UV + U2 + 3V2 = 0

Solving
-4UV + U2 + 3V2 = 0

Solving for variable 'U'.

Factor a trinomial.
(U + -3V)(U + -1V) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(U + -1V)' equal to zero and attempt to solve:

Simplifying
U + -1V = 0

Solving
U + -1V = 0

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

Add 'V' to each side of the equation.
U + -1V + V = 0 + V

Combine like terms: -1V + V = 0
U + 0 = 0 + V
U = 0 + V
Remove the zero:
U = V

Simplifying
U = V
Solution
U = {3V, V}