u^2-17uv+72v^2=0

Solution for u^2-17uv+72v^2=0 equation:

Simplifying
u2 + -17uv + 72v2 = 0

Reorder the terms:
-17uv + u2 + 72v2 = 0

Solving
-17uv + u2 + 72v2 = 0

Solving for variable 'u'.

Factor a trinomial.
(u + -9v)(u + -8v) = 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 + -8v)' equal to zero and attempt to solve:

Simplifying
u + -8v = 0

Solving
u + -8v = 0

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

Add '8v' to each side of the equation.
u + -8v + 8v = 0 + 8v

Combine like terms: -8v + 8v = 0
u + 0 = 0 + 8v
u = 0 + 8v
Remove the zero:
u = 8v

Simplifying
u = 8v
Solution
u = {9v, 8v}