(k+3)(k+6)=0

Solution for (k+3)(k+6)=0 equation:

Simplifying
(k + 3)(k + 6) = 0

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

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

Multiply (3 + k) * (6 + k)
(3(6 + k) + k(6 + k)) = 0
((6 * 3 + k * 3) + k(6 + k)) = 0
((18 + 3k) + k(6 + k)) = 0
(18 + 3k + (6 * k + k * k)) = 0
(18 + 3k + (6k + k2)) = 0

Combine like terms: 3k + 6k = 9k
(18 + 9k + k2) = 0

Solving
18 + 9k + k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(6 + k)(3 + 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 '(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
Solution
k = {-6, -3}