z=2zx+2zy

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Solution for z=2zx+2zy equation: 


Simplifying
z = 2zx + 2zy

Solving
z = 2xz + 2yz

Solving for variable 'z'.

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

Add '-2xz' to each side of the equation.
-2xz + z = 2xz + -2xz + 2yz

Combine like terms: 2xz + -2xz = 0
-2xz + z = 0 + 2yz
-2xz + z = 2yz

Add '-2yz' to each side of the equation.
-2xz + -2yz + z = 2yz + -2yz

Combine like terms: 2yz + -2yz = 0
-2xz + -2yz + z = 0

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


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

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0

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

Simplifying
-2x + -2y + 1 = 0

Reorder the terms:
1 + -2x + -2y = 0

Solving
1 + -2x + -2y = 0

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

Add '-1' to each side of the equation.
1 + -2x + -1 + -2y = 0 + -1

Reorder the terms:
1 + -1 + -2x + -2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x + -2y = 0 + -1
-2x + -2y = 0 + -1

Combine like terms: 0 + -1 = -1
-2x + -2y = -1

Add '2x' to each side of the equation.
-2x + 2x + -2y = -1 + 2x

Combine like terms: -2x + 2x = 0
0 + -2y = -1 + 2x
-2y = -1 + 2x

Add '2y' to each side of the equation.
-2y + 2y = -1 + 2x + 2y

Combine like terms: -2y + 2y = 0
0 = -1 + 2x + 2y

Simplifying
0 = -1 + 2x + 2y

The solution to this equation could not be determined.

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

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