(5z+8)(4+z)=0

Solution for (5z+8)(4+z)=0 equation:

Simplifying
(5z + 8)(4 + z) = 0

Reorder the terms:
(8 + 5z)(4 + z) = 0

Multiply (8 + 5z) * (4 + z)
(8(4 + z) + 5z * (4 + z)) = 0
((4 * 8 + z * 8) + 5z * (4 + z)) = 0
((32 + 8z) + 5z * (4 + z)) = 0
(32 + 8z + (4 * 5z + z * 5z)) = 0
(32 + 8z + (20z + 5z2)) = 0

Combine like terms: 8z + 20z = 28z
(32 + 28z + 5z2) = 0

Solving
32 + 28z + 5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(4 + z)(8 + 5z) = 0

Subproblem 1
Set the factor '(4 + z)' equal to zero and attempt to solve:

Simplifying
4 + z = 0

Solving
4 + z = 0

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

Add '-4' to each side of the equation.
4 + -4 + z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + z = 0 + -4
z = 0 + -4

Combine like terms: 0 + -4 = -4
z = -4

Simplifying
z = -4
Subproblem 2
Set the factor '(8 + 5z)' equal to zero and attempt to solve:

Simplifying
8 + 5z = 0

Solving
8 + 5z = 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 + 5z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5z = 0 + -8
5z = 0 + -8

Combine like terms: 0 + -8 = -8
5z = -8

Divide each side by '5'.
z = -1.6

Simplifying
z = -1.6
Solution
z = {-4, -1.6}