4x^2y^2-12xy+9=0

Solution for 4x^2y^2-12xy+9=0 equation:

Simplifying
4x2y2 + -12xy + 9 = 0

Reorder the terms:
9 + -12xy + 4x2y2 = 0

Solving
9 + -12xy + 4x2y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -2xy)(3 + -2xy) = 0

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

Simplifying
3 + -2xy = 0

Solving
3 + -2xy = 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 + -2xy = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2xy = 0 + -3
-2xy = 0 + -3

Combine like terms: 0 + -3 = -3
-2xy = -3

Divide each side by '-2y'.
x = 1.5y-1

Simplifying
x = 1.5y-1
Subproblem 2
Set the factor '(3 + -2xy)' equal to zero and attempt to solve:

Simplifying
3 + -2xy = 0

Solving
3 + -2xy = 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 + -2xy = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2xy = 0 + -3
-2xy = 0 + -3

Combine like terms: 0 + -3 = -3
-2xy = -3

Divide each side by '-2y'.
x = 1.5y-1

Simplifying
x = 1.5y-1
Solution
x = {1.5y-1, 1.5y-1}