(n+3)(3n+3)=

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

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

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

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

Multiply (3 + n) * (3 + 3n)
(3(3 + 3n) + n(3 + 3n)) = 0
((3 * 3 + 3n * 3) + n(3 + 3n)) = 0
((9 + 9n) + n(3 + 3n)) = 0
(9 + 9n + (3 * n + 3n * n)) = 0
(9 + 9n + (3n + 3n2)) = 0

Combine like terms: 9n + 3n = 12n
(9 + 12n + 3n2) = 0

Solving
9 + 12n + 3n2 = 0

Solving for variable 'n'.

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

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

Ignore the factor 3.
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}