(3xy+1)(2xy-3)=

Solution for (3xy+1)(2xy-3)= equation:

Simplifying
(3xy + 1)(2xy + -3) = 0

Reorder the terms:
(1 + 3xy)(2xy + -3) = 0

Reorder the terms:
(1 + 3xy)(-3 + 2xy) = 0

Multiply (1 + 3xy) * (-3 + 2xy)
(1(-3 + 2xy) + 3xy * (-3 + 2xy)) = 0
((-3 * 1 + 2xy * 1) + 3xy * (-3 + 2xy)) = 0
((-3 + 2xy) + 3xy * (-3 + 2xy)) = 0
(-3 + 2xy + (-3 * 3xy + 2xy * 3xy)) = 0
(-3 + 2xy + (-9xy + 6x2y2)) = 0

Combine like terms: 2xy + -9xy = -7xy
(-3 + -7xy + 6x2y2) = 0

Solving
-3 + -7xy + 6x2y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -3xy)(3 + -2xy) = 0

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

Simplifying
-1 + -3xy = 0

Solving
-1 + -3xy = 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 + -3xy = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3xy = 0 + 1
-3xy = 0 + 1

Combine like terms: 0 + 1 = 1
-3xy = 1

Divide each side by '-3y'.
x = -0.3333333333y-1

Simplifying
x = -0.3333333333y-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 = {-0.3333333333y-1, 1.5y-1}