4u^2+12uv-16v^2=0

Solution for 4u^2+12uv-16v^2=0 equation:

Simplifying
4u2 + 12uv + -16v2 = 0

Reorder the terms:
12uv + 4u2 + -16v2 = 0

Solving
12uv + 4u2 + -16v2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3uv + u2 + -4v2) = 0

Factor a trinomial.
4((u + -1v)(u + 4v)) = 0

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
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
Solution
u = {v, -4v}