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

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

Simplifying
x2y2 + xy + -6 = 0

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

Solving
-6 + xy + x2y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -1xy)(2 + -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 '(2 + -1xy)' equal to zero and attempt to solve:

Simplifying
2 + -1xy = 0

Solving
2 + -1xy = 0

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

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

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

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

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

Simplifying
x = 2y-1
Solution
x = {-3y-1, 2y-1}