x^2-14xy+45y^2=0

Solution for x^2-14xy+45y^2=0 equation:

Simplifying
x2 + -14xy + 45y2 = 0

Reorder the terms:
-14xy + x2 + 45y2 = 0

Solving
-14xy + x2 + 45y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -9y)(x + -5y) = 0

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

Simplifying
x + -9y = 0

Solving
x + -9y = 0

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

Add '9y' to each side of the equation.
x + -9y + 9y = 0 + 9y

Combine like terms: -9y + 9y = 0
x + 0 = 0 + 9y
x = 0 + 9y
Remove the zero:
x = 9y

Simplifying
x = 9y
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 = {9y, 5y}