(2z+5)(8+z)=0

Solution for (2z+5)(8+z)=0 equation:

Simplifying
(2z + 5)(8 + z) = 0

Reorder the terms:
(5 + 2z)(8 + z) = 0

Multiply (5 + 2z) * (8 + z)
(5(8 + z) + 2z * (8 + z)) = 0
((8 * 5 + z * 5) + 2z * (8 + z)) = 0
((40 + 5z) + 2z * (8 + z)) = 0
(40 + 5z + (8 * 2z + z * 2z)) = 0
(40 + 5z + (16z + 2z2)) = 0

Combine like terms: 5z + 16z = 21z
(40 + 21z + 2z2) = 0

Solving
40 + 21z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(8 + z)(5 + 2z) = 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 + 2z)' equal to zero and attempt to solve:

Simplifying
5 + 2z = 0

Solving
5 + 2z = 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 + 2z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2z = 0 + -5
2z = 0 + -5

Combine like terms: 0 + -5 = -5
2z = -5

Divide each side by '2'.
z = -2.5

Simplifying
z = -2.5
Solution
z = {-8, -2.5}