(z+3)(z+8)=0

Solution for (z+3)(z+8)=0 equation:

Simplifying
(z + 3)(z + 8) = 0

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

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

Multiply (3 + z) * (8 + z)
(3(8 + z) + z(8 + z)) = 0
((8 * 3 + z * 3) + z(8 + z)) = 0
((24 + 3z) + z(8 + z)) = 0
(24 + 3z + (8 * z + z * z)) = 0
(24 + 3z + (8z + z2)) = 0

Combine like terms: 3z + 8z = 11z
(24 + 11z + z2) = 0

Solving
24 + 11z + z2 = 0

Solving for variable 'z'.

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}