xy-zx=x

Solution for xy-zx=x equation:

Simplifying
xy + -1zx = x

Solving
xy + -1xz = x

Solving for variable 'x'.

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

Add '-1x' to each side of the equation.
xy + -1x + -1xz = x + -1x

Reorder the terms:
-1x + xy + -1xz = x + -1x

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

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

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-1 + y + -1z)' equal to zero and attempt to solve:

Simplifying
-1 + y + -1z = 0

Solving
-1 + y + -1z = 0

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

Add '1' to each side of the equation.
-1 + y + 1 + -1z = 0 + 1

Reorder the terms:
-1 + 1 + y + -1z = 0 + 1

Combine like terms: -1 + 1 = 0
0 + y + -1z = 0 + 1
y + -1z = 0 + 1

Combine like terms: 0 + 1 = 1
y + -1z = 1

Add '-1y' to each side of the equation.
y + -1y + -1z = 1 + -1y

Combine like terms: y + -1y = 0
0 + -1z = 1 + -1y
-1z = 1 + -1y

Add 'z' to each side of the equation.
-1z + z = 1 + -1y + z

Combine like terms: -1z + z = 0
0 = 1 + -1y + z

Simplifying
0 = 1 + -1y + z

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}