z^2+6z=-5

Solution for z^2+6z=-5 equation:

Simplifying
z2 + 6z = -5

Reorder the terms:
6z + z2 = -5

Solving
6z + z2 = -5

Solving for variable 'z'.

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

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

Factor a trinomial.
(5 + z)(1 + z) = 0

Subproblem 1
Set the factor '(5 + z)' equal to zero and attempt to solve:

Simplifying
5 + z = 0

Solving
5 + z = 0

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

Add '-5' to each side of the equation.
5 + -5 + z = 0 + -5

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

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

Simplifying
z = -5
Subproblem 2
Set the factor '(1 + z)' equal to zero and attempt to solve:

Simplifying
1 + z = 0

Solving
1 + z = 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 + z = 0 + -1

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

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

Simplifying
z = -1
Solution
z = {-5, -1}