(1[5z-8]1)(1[2+z]1)=0

Solution for (1[5z-8]1)(1[2+z]1)=0 equation:

Simplifying
(1[5z + -8] * 1)(1[2 + z] * 1) = 0

Reorder the terms:
(1[-8 + 5z] * 1)(1[2 + z] * 1) = 0

Reorder the terms for easier multiplication:
(1 * 1[-8 + 5z])(1[2 + z] * 1) = 0

Multiply 1 * 1
(1[-8 + 5z])(1[2 + z] * 1) = 0
([-8 * 1 + 5z * 1])(1[2 + z] * 1) = 0
([-8 + 5z])(1[2 + z] * 1) = 0

Reorder the terms for easier multiplication:
(-8 + 5z)(1 * 1[2 + z]) = 0

Multiply 1 * 1
(-8 + 5z)(1[2 + z]) = 0
(-8 + 5z)([2 * 1 + z * 1]) = 0
(-8 + 5z)([2 + 1z]) = 0

Multiply (-8 + 5z) * (2 + 1z)
(-8(2 + 1z) + 5z * (2 + 1z)) = 0
((2 * -8 + 1z * -8) + 5z * (2 + 1z)) = 0
((-16 + -8z) + 5z * (2 + 1z)) = 0
(-16 + -8z + (2 * 5z + 1z * 5z)) = 0
(-16 + -8z + (10z + 5z2)) = 0

Combine like terms: -8z + 10z = 2z
(-16 + 2z + 5z2) = 0

Solving
-16 + 2z + 5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-2 + -1z)(8 + -5z) = 0

Subproblem 1
Set the factor '(-2 + -1z)' equal to zero and attempt to solve:

Simplifying
-2 + -1z = 0

Solving
-2 + -1z = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1z = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1z = 0 + 2
-1z = 0 + 2

Combine like terms: 0 + 2 = 2
-1z = 2

Divide each side by '-1'.
z = -2

Simplifying
z = -2
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 = {-2, 1.6}