=3xy-6x(y-z)

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Solution for =3xy-6x(y-z) equation: 


Simplifying
0 = 3xy + -6x(y + -1z)
0 = 3xy + (y * -6x + -1z * -6x)
0 = 3xy + (-6xy + 6xz)

Combine like terms: 3xy + -6xy = -3xy
0 = -3xy + 6xz

Solving
0 = -3xy + 6xz

Solving for variable 'x'.

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

Add '3xy' to each side of the equation.
0 + 3xy = -3xy + 3xy + 6xz
Remove the zero:
3xy = -3xy + 3xy + 6xz

Combine like terms: -3xy + 3xy = 0
3xy = 0 + 6xz
3xy = 6xz

Add '-6xz' to each side of the equation.
3xy + -6xz = 6xz + -6xz

Combine like terms: 6xz + -6xz = 0
3xy + -6xz = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(y + -2z) = 0

Ignore the factor 3.

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

Simplifying
y + -2z = 0

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

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

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

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

Simplifying
0 = -1y + 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}

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