(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.
(3 + -1n)(6 + -1n) = 0

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

Simplifying
3 + -1n = 0

Solving
3 + -1n = 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 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 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 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

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