(z+8)(z+1)=0

Solution for (z+8)(z+1)=0 equation:

Simplifying
(z + 8)(z + 1) = 0

Reorder the terms:
(8 + z)(z + 1) = 0

Reorder the terms:
(8 + z)(1 + z) = 0

Multiply (8 + z) * (1 + z)
(8(1 + z) + z(1 + z)) = 0
((1 * 8 + z * 8) + z(1 + z)) = 0
((8 + 8z) + z(1 + z)) = 0
(8 + 8z + (1 * z + z * z)) = 0
(8 + 8z + (1z + z2)) = 0

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

Solving
8 + 9z + z2 = 0

Solving for variable 'z'.

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}