(k+3)(k+1)=0

Solution for (k+3)(k+1)=0 equation:

Simplifying
(k + 3)(k + 1) = 0

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

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

Multiply (3 + k) * (1 + k)
(3(1 + k) + k(1 + k)) = 0
((1 * 3 + k * 3) + k(1 + k)) = 0
((3 + 3k) + k(1 + k)) = 0
(3 + 3k + (1 * k + k * k)) = 0
(3 + 3k + (1k + k2)) = 0

Combine like terms: 3k + 1k = 4k
(3 + 4k + k2) = 0

Solving
3 + 4k + k2 = 0

Solving for variable 'k'.

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

Subproblem 1
Set the factor '(3 + k)' equal to zero and attempt to solve:

Simplifying
3 + k = 0

Solving
3 + k = 0

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

Add '-3' to each side of the equation.
3 + -3 + k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + k = 0 + -3
k = 0 + -3

Combine like terms: 0 + -3 = -3
k = -3

Simplifying
k = -3
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 = {-3, -1}