4xy^3+12xy^2+2x^2y^3=0

Solution for 4xy^3+12xy^2+2x^2y^3=0 equation:

Simplifying
4xy3 + 12xy2 + 2x2y3 = 0

Reorder the terms:
12xy2 + 4xy3 + 2x2y3 = 0

Solving
12xy2 + 4xy3 + 2x2y3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2xy2'.
2xy2(6 + 2y + xy) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'xy2' equal to zero and attempt to solve:

Simplifying
xy2 = 0

Solving
xy2 = 0

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

Simplifying
xy2 = 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 '(6 + 2y + xy)' equal to zero and attempt to solve:

Simplifying
6 + 2y + xy = 0

Reorder the terms:
6 + xy + 2y = 0

Solving
6 + xy + 2y = 0

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

Add '-6' to each side of the equation.
6 + xy + -6 + 2y = 0 + -6

Reorder the terms:
6 + -6 + xy + 2y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + xy + 2y = 0 + -6
xy + 2y = 0 + -6

Combine like terms: 0 + -6 = -6
xy + 2y = -6

Add '-2y' to each side of the equation.
xy + 2y + -2y = -6 + -2y

Combine like terms: 2y + -2y = 0
xy + 0 = -6 + -2y
xy = -6 + -2y

Divide each side by 'y'.
x = -6y-1 + -2

Simplifying
x = -6y-1 + -2

Reorder the terms:
x = -2 + -6y-1
Solution
x = {-2 + -6y-1}