2(x^2)y=2xyz

Solution for 2(x^2)y=2xyz equation:

Simplifying
2(x2) * y = 2xyz

Multiply x2 * y
2x2y = 2xyz

Solving
2x2y = 2xyz

Solving for variable 'x'.

Reorder the terms:
-2xyz + 2x2y = 2xyz + -2xyz

Combine like terms: 2xyz + -2xyz = 0
-2xyz + 2x2y = 0

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

Ignore the factor 2.
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 '(-1z + x)' equal to zero and attempt to solve:

Simplifying
-1z + x = 0

Reorder the terms:
x + -1z = 0

Solving
x + -1z = 0

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

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

Combine like terms: -1z + z = 0
x + 0 = 0 + z
x = 0 + z
Remove the zero:
x = z

Simplifying
x = z
Solution
x = {z}