(z+5)*(z+8)=

Solution for (z+5)*(z+8)= equation:

Simplifying
(z + 5)(z + 8) = 0

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

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

Multiply (5 + z) * (8 + z)
(5(8 + z) + z(8 + z)) = 0
((8 * 5 + z * 5) + z(8 + z)) = 0
((40 + 5z) + z(8 + z)) = 0
(40 + 5z + (8 * z + z * z)) = 0
(40 + 5z + (8z + z2)) = 0

Combine like terms: 5z + 8z = 13z
(40 + 13z + z2) = 0

Solving
40 + 13z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(8 + z)(5 + 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 '(5 + z)' equal to zero and attempt to solve:

Simplifying
5 + z = 0

Solving
5 + z = 0

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

Add '-5' to each side of the equation.
5 + -5 + z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + z = 0 + -5
z = 0 + -5

Combine like terms: 0 + -5 = -5
z = -5

Simplifying
z = -5
Solution
z = {-8, -5}