12y+6=6(zy+1)

Solution for 12y+6=6(zy+1) equation:

Simplifying
12y + 6 = 6(zy + 1)

Reorder the terms:
6 + 12y = 6(zy + 1)

Reorder the terms:
6 + 12y = 6(1 + yz)
6 + 12y = (1 * 6 + yz * 6)
6 + 12y = (6 + 6yz)

Add '-6' to each side of the equation.
6 + -6 + 12y = 6 + -6 + 6yz

Combine like terms: 6 + -6 = 0
0 + 12y = 6 + -6 + 6yz
12y = 6 + -6 + 6yz

Combine like terms: 6 + -6 = 0
12y = 0 + 6yz
12y = 6yz

Solving
12y = 6yz

Solving for variable 'y'.

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

Add '-6yz' to each side of the equation.
12y + -6yz = 6yz + -6yz

Combine like terms: 6yz + -6yz = 0
12y + -6yz = 0

Factor out the Greatest Common Factor (GCF), '6y'.
6y(2 + -1z) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

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

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

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

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

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

Simplifying
0 = -2 + z

The solution to this equation could not be determined.

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