6x^2y^2+5xy-6=0

Solution for 6x^2y^2+5xy-6=0 equation:

Simplifying
6x2y2 + 5xy + -6 = 0

Reorder the terms:
-6 + 5xy + 6x2y2 = 0

Solving
-6 + 5xy + 6x2y2 = 0

Solving for variable 'x'.

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

Simplifying
2 + -3xy = 0

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

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

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

Divide each side by '-3y'.
x = 0.6666666667y-1

Simplifying
x = 0.6666666667y-1
Solution
x = {-1.5y-1, 0.6666666667y-1}