x^2y^2-6xy+9=0

Solution for x^2y^2-6xy+9=0 equation:

Simplifying
x2y2 + -6xy + 9 = 0

Reorder the terms:
9 + -6xy + x2y2 = 0

Solving
9 + -6xy + x2y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -1xy)(3 + -1xy) = 0

Subproblem 1
Set the factor '(3 + -1xy)' equal to zero and attempt to solve:

Simplifying
3 + -1xy = 0

Solving
3 + -1xy = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1xy = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1xy = 0 + -3
-1xy = 0 + -3

Combine like terms: 0 + -3 = -3
-1xy = -3

Divide each side by '-1y'.
x = 3y-1

Simplifying
x = 3y-1
Subproblem 2
Set the factor '(3 + -1xy)' equal to zero and attempt to solve:

Simplifying
3 + -1xy = 0

Solving
3 + -1xy = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1xy = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1xy = 0 + -3
-1xy = 0 + -3

Combine like terms: 0 + -3 = -3
-1xy = -3

Divide each side by '-1y'.
x = 3y-1

Simplifying
x = 3y-1
Solution
x = {3y-1, 3y-1}