(n+6)(n+3)=0

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

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

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

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

Multiply (6 + n) * (3 + n)
(6(3 + n) + n(3 + n)) = 0
((3 * 6 + n * 6) + n(3 + n)) = 0
((18 + 6n) + n(3 + n)) = 0
(18 + 6n + (3 * n + n * n)) = 0
(18 + 6n + (3n + n2)) = 0

Combine like terms: 6n + 3n = 9n
(18 + 9n + n2) = 0

Solving
18 + 9n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(6 + n)(3 + n) = 0

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

Simplifying
6 + n = 0

Solving
6 + n = 0

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

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

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

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

Simplifying
n = -6
Subproblem 2
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

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

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

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

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

Simplifying
n = -3
Solution
n = {-6, -3}