z^2+8z=-15

Solution for z^2+8z=-15 equation:

Simplifying
z2 + 8z = -15

Reorder the terms:
8z + z2 = -15

Solving
8z + z2 = -15

Solving for variable 'z'.

Reorder the terms:
15 + 8z + z2 = -15 + 15

Combine like terms: -15 + 15 = 0
15 + 8z + z2 = 0

Factor a trinomial.
(5 + z)(3 + 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 '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

Solving
3 + z = 0

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

Add '-3' to each side of the equation.
3 + -3 + z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + z = 0 + -3
z = 0 + -3

Combine like terms: 0 + -3 = -3
z = -3

Simplifying
z = -3
Solution
z = {-5, -3}