(6n+9)(3n+3)=0

Solution for (6n+9)(3n+3)=0 equation:

Simplifying
(6n + 9)(3n + 3) = 0

Reorder the terms:
(9 + 6n)(3n + 3) = 0

Reorder the terms:
(9 + 6n)(3 + 3n) = 0

Multiply (9 + 6n) * (3 + 3n)
(9(3 + 3n) + 6n * (3 + 3n)) = 0
((3 * 9 + 3n * 9) + 6n * (3 + 3n)) = 0
((27 + 27n) + 6n * (3 + 3n)) = 0
(27 + 27n + (3 * 6n + 3n * 6n)) = 0
(27 + 27n + (18n + 18n2)) = 0

Combine like terms: 27n + 18n = 45n
(27 + 45n + 18n2) = 0

Solving
27 + 45n + 18n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '9'.
9(3 + 5n + 2n2) = 0

Factor a trinomial.
9((3 + 2n)(1 + n)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(3 + 2n)' equal to zero and attempt to solve:

Simplifying
3 + 2n = 0

Solving
3 + 2n = 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 + 2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2n = 0 + -3
2n = 0 + -3

Combine like terms: 0 + -3 = -3
2n = -3

Divide each side by '2'.
n = -1.5

Simplifying
n = -1.5
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 = {-1.5, -1}