z^2+11z=-24

Solution for z^2+11z=-24 equation:

Simplifying
z2 + 11z = -24

Reorder the terms:
11z + z2 = -24

Solving
11z + z2 = -24

Solving for variable 'z'.

Reorder the terms:
24 + 11z + z2 = -24 + 24

Combine like terms: -24 + 24 = 0
24 + 11z + z2 = 0

Factor a trinomial.
(8 + z)(3 + 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 '(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 = {-8, -3}