10xyz+10xy-5xz-5x=0

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Solution for 10xyz+10xy-5xz-5x=0 equation: 


Simplifying
10xyz + 10xy + -5xz + -5x = 0

Reorder the terms:
-5x + 10xy + 10xyz + -5xz = 0

Solving
-5x + 10xy + 10xyz + -5xz = 0

Solving for variable 'x'.

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

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-1 + 2y + 2yz + -1z) = 0

Ignore the factor 5.

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 + 2y + 2yz + -1z)' equal to zero and attempt to solve:

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

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

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

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

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

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

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

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

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

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

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

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

Simplifying
0 = 1 + -2y + -2yz + 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}

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