x^2-12xy+35y^2=0

Solution for x^2-12xy+35y^2=0 equation:

Simplifying
x2 + -12xy + 35y2 = 0

Reorder the terms:
-12xy + x2 + 35y2 = 0

Solving
-12xy + x2 + 35y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -7y)(x + -5y) = 0

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

Simplifying
x + -7y = 0

Solving
x + -7y = 0

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

Add '7y' to each side of the equation.
x + -7y + 7y = 0 + 7y

Combine like terms: -7y + 7y = 0
x + 0 = 0 + 7y
x = 0 + 7y
Remove the zero:
x = 7y

Simplifying
x = 7y
Subproblem 2
Set the factor '(x + -5y)' equal to zero and attempt to solve:

Simplifying
x + -5y = 0

Solving
x + -5y = 0

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

Add '5y' to each side of the equation.
x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
x + 0 = 0 + 5y
x = 0 + 5y
Remove the zero:
x = 5y

Simplifying
x = 5y
Solution
x = {7y, 5y}