(1[5z+8]1)(1[4+z]1)=0

Solution for (1[5z+8]1)(1[4+z]1)=0 equation:

Simplifying
(1[5z + 8] * 1)(1[4 + z] * 1) = 0

Reorder the terms:
(1[8 + 5z] * 1)(1[4 + z] * 1) = 0

Reorder the terms for easier multiplication:
(1 * 1[8 + 5z])(1[4 + z] * 1) = 0

Multiply 1 * 1
(1[8 + 5z])(1[4 + z] * 1) = 0
([8 * 1 + 5z * 1])(1[4 + z] * 1) = 0
([8 + 5z])(1[4 + z] * 1) = 0

Reorder the terms for easier multiplication:
(8 + 5z)(1 * 1[4 + z]) = 0

Multiply 1 * 1
(8 + 5z)(1[4 + z]) = 0
(8 + 5z)([4 * 1 + z * 1]) = 0
(8 + 5z)([4 + 1z]) = 0

Multiply (8 + 5z) * (4 + 1z)
(8(4 + 1z) + 5z * (4 + 1z)) = 0
((4 * 8 + 1z * 8) + 5z * (4 + 1z)) = 0
((32 + 8z) + 5z * (4 + 1z)) = 0
(32 + 8z + (4 * 5z + 1z * 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}