4x^2y^2-4xy=-1

Solution for 4x^2y^2-4xy=-1 equation:

Simplifying
4x2y2 + -4xy = -1

Reorder the terms:
-4xy + 4x2y2 = -1

Solving
-4xy + 4x2y2 = -1

Solving for variable 'x'.

Reorder the terms:
1 + -4xy + 4x2y2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -4xy + 4x2y2 = 0

Factor a trinomial.
(1 + -2xy)(1 + -2xy) = 0

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

Simplifying
1 + -2xy = 0

Solving
1 + -2xy = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2xy = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2xy = 0 + -1
-2xy = 0 + -1

Combine like terms: 0 + -1 = -1
-2xy = -1

Divide each side by '-2y'.
x = 0.5y-1

Simplifying
x = 0.5y-1
Subproblem 2
Set the factor '(1 + -2xy)' equal to zero and attempt to solve:

Simplifying
1 + -2xy = 0

Solving
1 + -2xy = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2xy = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2xy = 0 + -1
-2xy = 0 + -1

Combine like terms: 0 + -1 = -1
-2xy = -1

Divide each side by '-2y'.
x = 0.5y-1

Simplifying
x = 0.5y-1
Solution
x = {0.5y-1, 0.5y-1}