(3xy-1)(4xy+2)=

Solution for (3xy-1)(4xy+2)= equation:

Simplifying
(3xy + -1)(4xy + 2) = 0

Reorder the terms:
(-1 + 3xy)(4xy + 2) = 0

Reorder the terms:
(-1 + 3xy)(2 + 4xy) = 0

Multiply (-1 + 3xy) * (2 + 4xy)
(-1(2 + 4xy) + 3xy * (2 + 4xy)) = 0
((2 * -1 + 4xy * -1) + 3xy * (2 + 4xy)) = 0
((-2 + -4xy) + 3xy * (2 + 4xy)) = 0
(-2 + -4xy + (2 * 3xy + 4xy * 3xy)) = 0
(-2 + -4xy + (6xy + 12x2y2)) = 0

Combine like terms: -4xy + 6xy = 2xy
(-2 + 2xy + 12x2y2) = 0

Solving
-2 + 2xy + 12x2y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + xy + 6x2y2) = 0

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

Ignore the factor 2.
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 + -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
Solution
x = {-0.5y-1, 0.3333333333y-1}