z^2+6z=-8

Solution for z^2+6z=-8 equation:

Simplifying
z2 + 6z = -8

Reorder the terms:
6z + z2 = -8

Solving
6z + z2 = -8

Solving for variable 'z'.

Reorder the terms:
8 + 6z + z2 = -8 + 8

Combine like terms: -8 + 8 = 0
8 + 6z + z2 = 0

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

Subproblem 1
Set the factor '(4 + z)' equal to zero and attempt to solve:

Simplifying
4 + z = 0

Solving
4 + z = 0

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

Add '-4' to each side of the equation.
4 + -4 + z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + z = 0 + -4
z = 0 + -4

Combine like terms: 0 + -4 = -4
z = -4

Simplifying
z = -4
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 = {-4, -2}