=4x^3y-4x^2y-8xy

Solution for =4x^3y-4x^2y-8xy equation:

Simplifying
0 = 4x3y + -4x2y + -8xy

Reorder the terms:
0 = -8xy + -4x2y + 4x3y

Solving
0 = -8xy + -4x2y + 4x3y

Solving for variable 'x'.
Remove the zero:
8xy + 4x2y + -4x3y = -8xy + -4x2y + 4x3y + 8xy + 4x2y + -4x3y

Reorder the terms:
8xy + 4x2y + -4x3y = -8xy + 8xy + -4x2y + 4x2y + 4x3y + -4x3y

Combine like terms: -8xy + 8xy = 0
8xy + 4x2y + -4x3y = 0 + -4x2y + 4x2y + 4x3y + -4x3y
8xy + 4x2y + -4x3y = -4x2y + 4x2y + 4x3y + -4x3y

Combine like terms: -4x2y + 4x2y = 0
8xy + 4x2y + -4x3y = 0 + 4x3y + -4x3y
8xy + 4x2y + -4x3y = 4x3y + -4x3y

Combine like terms: 4x3y + -4x3y = 0
8xy + 4x2y + -4x3y = 0

Factor out the Greatest Common Factor (GCF), '4xy'.
4xy(2 + x + -1x2) = 0

Factor a trinomial.
4xy((2 + -1x)(1 + x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'xy' equal to zero and attempt to solve:

Simplifying
xy = 0

Solving
xy = 0

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

Simplifying
xy = 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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 3
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {2, -1}