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

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

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

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

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

Combine like terms: 20z + 8z = 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}