2u^2+3uv-2v^2=0

Solution for 2u^2+3uv-2v^2=0 equation:

Simplifying
2u2 + 3uv + -2v2 = 0

Reorder the terms:
3uv + 2u2 + -2v2 = 0

Solving
3uv + 2u2 + -2v2 = 0

Solving for variable 'u'.

Factor a trinomial.
(2u + -1v)(u + 2v) = 0

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

Simplifying
2u + -1v = 0

Solving
2u + -1v = 0

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

Add 'v' to each side of the equation.
2u + -1v + v = 0 + v

Combine like terms: -1v + v = 0
2u + 0 = 0 + v
2u = 0 + v
Remove the zero:
2u = v

Divide each side by '2'.
u = 0.5v

Simplifying
u = 0.5v
Subproblem 2
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
Solution
u = {0.5v, -2v}