(k+5)(k+6)=0

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

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

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

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

Multiply (5 + k) * (6 + k)
(5(6 + k) + k(6 + k)) = 0
((6 * 5 + k * 5) + k(6 + k)) = 0
((30 + 5k) + k(6 + k)) = 0
(30 + 5k + (6 * k + k * k)) = 0
(30 + 5k + (6k + k2)) = 0

Combine like terms: 5k + 6k = 11k
(30 + 11k + k2) = 0

Solving
30 + 11k + k2 = 0

Solving for variable 'k'.

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

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

Simplifying
6 + k = 0

Solving
6 + k = 0

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

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

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

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

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

Simplifying
5 + k = 0

Solving
5 + k = 0

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

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

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

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

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