(2n+2)(3n+9)=0

Solution for (2n+2)(3n+9)=0 equation:

Simplifying
(2n + 2)(3n + 9) = 0

Reorder the terms:
(2 + 2n)(3n + 9) = 0

Reorder the terms:
(2 + 2n)(9 + 3n) = 0

Multiply (2 + 2n) * (9 + 3n)
(2(9 + 3n) + 2n * (9 + 3n)) = 0
((9 * 2 + 3n * 2) + 2n * (9 + 3n)) = 0
((18 + 6n) + 2n * (9 + 3n)) = 0
(18 + 6n + (9 * 2n + 3n * 2n)) = 0
(18 + 6n + (18n + 6n2)) = 0

Combine like terms: 6n + 18n = 24n
(18 + 24n + 6n2) = 0

Solving
18 + 24n + 6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + 4n + n2) = 0

Factor a trinomial.
6((3 + n)(1 + n)) = 0

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

Solving
1 + n = 0

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

Add '-1' to each side of the equation.
1 + -1 + n = 0 + -1

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

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

Simplifying
n = -1
Solution
n = {-3, -1}