z^2+15z+24=-32

Solution for z^2+15z+24=-32 equation:

Simplifying
z2 + 15z + 24 = -32

Reorder the terms:
24 + 15z + z2 = -32

Solving
24 + 15z + z2 = -32

Solving for variable 'z'.

Reorder the terms:
24 + 32 + 15z + z2 = -32 + 32

Combine like terms: 24 + 32 = 56
56 + 15z + z2 = -32 + 32

Combine like terms: -32 + 32 = 0
56 + 15z + z2 = 0

Factor a trinomial.
(8 + z)(7 + z) = 0

Subproblem 1
Set the factor '(8 + z)' equal to zero and attempt to solve:

Simplifying
8 + z = 0

Solving
8 + z = 0

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

Add '-8' to each side of the equation.
8 + -8 + z = 0 + -8

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

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

Simplifying
z = -8
Subproblem 2
Set the factor '(7 + z)' equal to zero and attempt to solve:

Simplifying
7 + z = 0

Solving
7 + z = 0

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

Add '-7' to each side of the equation.
7 + -7 + z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + z = 0 + -7
z = 0 + -7

Combine like terms: 0 + -7 = -7
z = -7

Simplifying
z = -7
Solution
z = {-8, -7}