3xy^2(2x^2y-3y)=

Solution for 3xy^2(2x^2y-3y)= equation:

Simplifying
3xy2(2x2y + -3y) = 0
(2x2y * 3xy2 + -3y * 3xy2) = 0

Reorder the terms:
(-9xy3 + 6x3y3) = 0
(-9xy3 + 6x3y3) = 0

Solving
-9xy3 + 6x3y3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3xy3'.
3xy3(-3 + 2x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'xy3' equal to zero and attempt to solve:

Simplifying
xy3 = 0

Solving
xy3 = 0

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

Simplifying
xy3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-3 + 2x2)' equal to zero and attempt to solve:

Simplifying
-3 + 2x2 = 0

Solving
-3 + 2x2 = 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 + 2x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2x2 = 0 + 3
2x2 = 0 + 3

Combine like terms: 0 + 3 = 3
2x2 = 3

Divide each side by '2'.
x2 = 1.5

Simplifying
x2 = 1.5

Take the square root of each side:
x = {-1.224744871, 1.224744871}
Solution
x = {-1.224744871, 1.224744871}