5u^2-35uv+60v^2=0

Solution for 5u^2-35uv+60v^2=0 equation:

Simplifying
5u2 + -35uv + 60v2 = 0

Reorder the terms:
-35uv + 5u2 + 60v2 = 0

Solving
-35uv + 5u2 + 60v2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-7uv + u2 + 12v2) = 0

Factor a trinomial.
5((u + -4v)(u + -3v)) = 0

Ignore the factor 5.
Subproblem 1
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
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 = {4v, 3v}