20x^2y^2+23xy+6=0

Solution for 20x^2y^2+23xy+6=0 equation:

Simplifying
20x2y2 + 23xy + 6 = 0

Reorder the terms:
6 + 23xy + 20x2y2 = 0

Solving
6 + 23xy + 20x2y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + 4xy)(2 + 5xy) = 0

Subproblem 1
Set the factor '(3 + 4xy)' equal to zero and attempt to solve:

Simplifying
3 + 4xy = 0

Solving
3 + 4xy = 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 + 4xy = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4xy = 0 + -3
4xy = 0 + -3

Combine like terms: 0 + -3 = -3
4xy = -3

Divide each side by '4y'.
x = -0.75y-1

Simplifying
x = -0.75y-1
Subproblem 2
Set the factor '(2 + 5xy)' equal to zero and attempt to solve:

Simplifying
2 + 5xy = 0

Solving
2 + 5xy = 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 + 5xy = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5xy = 0 + -2
5xy = 0 + -2

Combine like terms: 0 + -2 = -2
5xy = -2

Divide each side by '5y'.
x = -0.4y-1

Simplifying
x = -0.4y-1
Solution
x = {-0.75y-1, -0.4y-1}