(1[2+z]1)(1[5z+6]1)=0

Solution for (1[2+z]1)(1[5z+6]1)=0 equation:

Simplifying
(1[2 + z] * 1)(1[5z + 6] * 1) = 0

Reorder the terms for easier multiplication:
(1 * 1[2 + z])(1[5z + 6] * 1) = 0

Multiply 1 * 1
(1[2 + z])(1[5z + 6] * 1) = 0
([2 * 1 + z * 1])(1[5z + 6] * 1) = 0
([2 + 1z])(1[5z + 6] * 1) = 0

Reorder the terms:
(2 + 1z)(1[6 + 5z] * 1) = 0

Reorder the terms for easier multiplication:
(2 + 1z)(1 * 1[6 + 5z]) = 0

Multiply 1 * 1
(2 + 1z)(1[6 + 5z]) = 0
(2 + 1z)([6 * 1 + 5z * 1]) = 0
(2 + 1z)([6 + 5z]) = 0

Multiply (2 + 1z) * (6 + 5z)
(2(6 + 5z) + 1z * (6 + 5z)) = 0
((6 * 2 + 5z * 2) + 1z * (6 + 5z)) = 0
((12 + 10z) + 1z * (6 + 5z)) = 0
(12 + 10z + (6 * 1z + 5z * 1z)) = 0
(12 + 10z + (6z + 5z2)) = 0

Combine like terms: 10z + 6z = 16z
(12 + 16z + 5z2) = 0

Solving
12 + 16z + 5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(2 + z)(6 + 5z) = 0

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

Simplifying
2 + z = 0

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

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

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

Simplifying
z = -2
Subproblem 2
Set the factor '(6 + 5z)' equal to zero and attempt to solve:

Simplifying
6 + 5z = 0

Solving
6 + 5z = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5z = 0 + -6
5z = 0 + -6

Combine like terms: 0 + -6 = -6
5z = -6

Divide each side by '5'.
z = -1.2

Simplifying
z = -1.2
Solution
z = {-2, -1.2}