x=yx

Solution for x=yx equation:

Simplifying
x = yx

Solving
x = xy

Solving for variable 'x'.

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

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -1y) = 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 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

Solving
1 + -1y = 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 + -1y = 0 + -1

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

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

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

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

Simplifying
0 = -1 + y

The solution to this equation could not be determined.

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