u^2-6uv-27v^2=0

Solution for u^2-6uv-27v^2=0 equation:

Simplifying
u2 + -6uv + -27v2 = 0

Reorder the terms:
-6uv + u2 + -27v2 = 0

Solving
-6uv + u2 + -27v2 = 0

Solving for variable 'u'.

Factor a trinomial.
(u + -9v)(u + 3v) = 0

Subproblem 1
Set the factor '(u + -9v)' equal to zero and attempt to solve:

Simplifying
u + -9v = 0

Solving
u + -9v = 0

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

Add '9v' to each side of the equation.
u + -9v + 9v = 0 + 9v

Combine like terms: -9v + 9v = 0
u + 0 = 0 + 9v
u = 0 + 9v
Remove the zero:
u = 9v

Simplifying
u = 9v
Subproblem 2
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
Solution
u = {9v, -3v}