8=-z^2-9z

Solution for 8=-z^2-9z equation:

Simplifying
8 = -1z2 + -9z

Reorder the terms:
8 = -9z + -1z2

Solving
8 = -9z + -1z2

Solving for variable 'z'.

Reorder the terms:
8 + 9z + z2 = -9z + 9z + -1z2 + z2

Combine like terms: -9z + 9z = 0
8 + 9z + z2 = 0 + -1z2 + z2
8 + 9z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
8 + 9z + z2 = 0

Factor a trinomial.
(8 + z)(1 + 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 '(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 = {-8, -1}