(n+3)(3n+1)=0

Solution for (n+3)(3n+1)=0 equation:

Simplifying
(n + 3)(3n + 1) = 0

Reorder the terms:
(3 + n)(3n + 1) = 0

Reorder the terms:
(3 + n)(1 + 3n) = 0

Multiply (3 + n) * (1 + 3n)
(3(1 + 3n) + n(1 + 3n)) = 0
((1 * 3 + 3n * 3) + n(1 + 3n)) = 0
((3 + 9n) + n(1 + 3n)) = 0
(3 + 9n + (1 * n + 3n * n)) = 0
(3 + 9n + (1n + 3n2)) = 0

Combine like terms: 9n + 1n = 10n
(3 + 10n + 3n2) = 0

Solving
3 + 10n + 3n2 = 0

Solving for variable 'n'.

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

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 + 3n)' equal to zero and attempt to solve:

Simplifying
1 + 3n = 0

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

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

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

Divide each side by '3'.
n = -0.3333333333

Simplifying
n = -0.3333333333
Solution
n = {-3, -0.3333333333}