(k+3)(k+2)=0

Solution for (k+3)(k+2)=0 equation:

Simplifying
(k + 3)(k + 2) = 0

Reorder the terms:
(3 + k)(k + 2) = 0

Reorder the terms:
(3 + k)(2 + k) = 0

Multiply (3 + k) * (2 + k)
(3(2 + k) + k(2 + k)) = 0
((2 * 3 + k * 3) + k(2 + k)) = 0
((6 + 3k) + k(2 + k)) = 0
(6 + 3k + (2 * k + k * k)) = 0
(6 + 3k + (2k + k2)) = 0

Combine like terms: 3k + 2k = 5k
(6 + 5k + k2) = 0

Solving
6 + 5k + k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(3 + k)(2 + 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 '(2 + k)' equal to zero and attempt to solve:

Simplifying
2 + k = 0

Solving
2 + k = 0

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

Add '-2' to each side of the equation.
2 + -2 + k = 0 + -2

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

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

Simplifying
k = -2
Solution
k = {-3, -2}