(k+1)(k+5)=0

Solution for (k+1)(k+5)=0 equation:

Simplifying
(k + 1)(k + 5) = 0

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

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

Multiply (1 + k) * (5 + k)
(1(5 + k) + k(5 + k)) = 0
((5 * 1 + k * 1) + k(5 + k)) = 0
((5 + 1k) + k(5 + k)) = 0
(5 + 1k + (5 * k + k * k)) = 0
(5 + 1k + (5k + k2)) = 0

Combine like terms: 1k + 5k = 6k
(5 + 6k + k2) = 0

Solving
5 + 6k + k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(5 + k)(1 + k) = 0

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

Simplifying
1 + k = 0

Solving
1 + k = 0

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

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

Combine like terms: 1 + -1 = 0
0 + k = 0 + -1
k = 0 + -1

Combine like terms: 0 + -1 = -1
k = -1

Simplifying
k = -1
Solution
k = {-5, -1}