z^2+z=6+6z

Solution for z^2+z=6+6z equation:

Simplifying
z2 + z = 6 + 6z

Reorder the terms:
z + z2 = 6 + 6z

Solving
z + z2 = 6 + 6z

Solving for variable 'z'.

Reorder the terms:
-6 + z + -6z + z2 = 6 + 6z + -6 + -6z

Combine like terms: z + -6z = -5z
-6 + -5z + z2 = 6 + 6z + -6 + -6z

Reorder the terms:
-6 + -5z + z2 = 6 + -6 + 6z + -6z

Combine like terms: 6 + -6 = 0
-6 + -5z + z2 = 0 + 6z + -6z
-6 + -5z + z2 = 6z + -6z

Combine like terms: 6z + -6z = 0
-6 + -5z + z2 = 0

Factor a trinomial.
(-1 + -1z)(6 + -1z) = 0

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

Simplifying
-1 + -1z = 0

Solving
-1 + -1z = 0

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

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

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

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

Divide each side by '-1'.
z = -1

Simplifying
z = -1
Subproblem 2
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z = 0 + -6
-1z = 0 + -6

Combine like terms: 0 + -6 = -6
-1z = -6

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Solution
z = {-1, 6}