(x*z*2)+(x*y)=(y*z*x)

Solution for (x*z*2)+(x*y)=(y*z*x) equation:

Simplifying
(x * z * 2) + (x * y) = (y * z * x)

Reorder the terms for easier multiplication:
(2x * z) + (x * y) = (y * z * x)

Multiply x * z
(2xz) + (x * y) = (y * z * x)

Multiply x * y
(2xz) + (xy) = (y * z * x)
(2xz) + xy = (y * z * x)

Reorder the terms:
xy + (2xz) = (y * z * x)

Multiply y * z
xy + (2xz) = (yz * x)

Multiply yz * x
xy + (2xz) = (xyz)
xy + (2xz) = xyz

Solving
xy + (2xz) = xyz

Solving for variable 'x'.

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

Add '-1xyz' to each side of the equation.
xy + -1xyz + (2xz) = xyz + -1xyz

Combine like terms: xyz + -1xyz = 0
xy + -1xyz + (2xz) = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(y + -1yz + (2z)) = 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 '(y + -1yz + (2z))' equal to zero and attempt to solve:

Simplifying
y + -1yz + (2z) = 0

Solving
y + -1yz + (2z) = 0

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

Add '-1y' to each side of the equation.
y + -1yz + -1y + (2z) = 0 + -1y

Reorder the terms:
y + -1y + -1yz + (2z) = 0 + -1y

Combine like terms: y + -1y = 0
0 + -1yz + (2z) = 0 + -1y
-1yz + (2z) = 0 + -1y
Remove the zero:
-1yz + (2z) = -1y

Add 'yz' to each side of the equation.
-1yz + yz + (2z) = -1y + yz

Combine like terms: -1yz + yz = 0
0 + (2z) = -1y + yz
(2z) = -1y + yz

Add '(-2z)' to each side of the equation.
(2z) + (-2z) = -1y + yz + (-2z)

Combine like terms: (2z) + (-2z) = 0
0 = -1y + yz + (-2z)

Simplifying
0 = -1y + yz + (-2z)

The solution to this equation could not be determined.

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