z^2+6z=-12-2z

Solution for z^2+6z=-12-2z equation:

Simplifying
z2 + 6z = -12 + -2z

Reorder the terms:
6z + z2 = -12 + -2z

Solving
6z + z2 = -12 + -2z

Solving for variable 'z'.

Reorder the terms:
12 + 6z + 2z + z2 = -12 + -2z + 12 + 2z

Combine like terms: 6z + 2z = 8z
12 + 8z + z2 = -12 + -2z + 12 + 2z

Reorder the terms:
12 + 8z + z2 = -12 + 12 + -2z + 2z

Combine like terms: -12 + 12 = 0
12 + 8z + z2 = 0 + -2z + 2z
12 + 8z + z2 = -2z + 2z

Combine like terms: -2z + 2z = 0
12 + 8z + z2 = 0

Factor a trinomial.
(6 + z)(2 + z) = 0

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

Simplifying
6 + z = 0

Solving
6 + z = 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 + z = 0 + -6

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

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

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

Simplifying
2 + z = 0

Solving
2 + z = 0

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

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

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

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

Simplifying
z = -2
Solution
z = {-6, -2}