xyz+yxz-zyx-x^2yz=

Solution for xyz+yxz-zyx-x^2yz= equation:

Simplifying
xyz + yxz + -1zyx + -1x2yz = 0

Combine like terms: xyz + xyz = 2xyz
2xyz + -1xyz + -1x2yz = 0

Combine like terms: 2xyz + -1xyz = 1xyz
1xyz + -1x2yz = 0

Solving
1xyz + -1x2yz = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'xyz'.
xyz(1 + -1x) = 0

Subproblem 1
Set the factor 'xyz' equal to zero and attempt to solve:

Simplifying
xyz = 0

Solving
xyz = 0

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

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {1}