(z+5)(z+6)=0

Solution for (z+5)(z+6)=0 equation:

Simplifying
(z + 5)(z + 6) = 0

Reorder the terms:
(5 + z)(z + 6) = 0

Reorder the terms:
(5 + z)(6 + z) = 0

Multiply (5 + z) * (6 + z)
(5(6 + z) + z(6 + z)) = 0
((6 * 5 + z * 5) + z(6 + z)) = 0
((30 + 5z) + z(6 + z)) = 0
(30 + 5z + (6 * z + z * z)) = 0
(30 + 5z + (6z + z2)) = 0

Combine like terms: 5z + 6z = 11z
(30 + 11z + z2) = 0

Solving
30 + 11z + z2 = 0

Solving for variable 'z'.

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

Subproblem 1
Set the factor '(6 + z)' equal to zero and attempt to solve:

Simplifying
6 + z = 0

Solving
6 + z = 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 + z = 0 + -6

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

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

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

Simplifying
5 + z = 0

Solving
5 + z = 0

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

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

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

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

Simplifying
z = -5
Solution
z = {-6, -5}