u^2-5uv-14v^2=0

Solution for u^2-5uv-14v^2=0 equation:

Simplifying
u2 + -5uv + -14v2 = 0

Reorder the terms:
-5uv + u2 + -14v2 = 0

Solving
-5uv + u2 + -14v2 = 0

Solving for variable 'u'.

Factor a trinomial.
(u + -7v)(u + 2v) = 0

Subproblem 1
Set the factor '(u + -7v)' equal to zero and attempt to solve:

Simplifying
u + -7v = 0

Solving
u + -7v = 0

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

Add '7v' to each side of the equation.
u + -7v + 7v = 0 + 7v

Combine like terms: -7v + 7v = 0
u + 0 = 0 + 7v
u = 0 + 7v
Remove the zero:
u = 7v

Simplifying
u = 7v
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 = {7v, -2v}