(3n+1)(n+4)=0

Solution for (3n+1)(n+4)=0 equation:

Simplifying
(3n + 1)(n + 4) = 0

Reorder the terms:
(1 + 3n)(n + 4) = 0

Reorder the terms:
(1 + 3n)(4 + n) = 0

Multiply (1 + 3n) * (4 + n)
(1(4 + n) + 3n * (4 + n)) = 0
((4 * 1 + n * 1) + 3n * (4 + n)) = 0
((4 + 1n) + 3n * (4 + n)) = 0
(4 + 1n + (4 * 3n + n * 3n)) = 0
(4 + 1n + (12n + 3n2)) = 0

Combine like terms: 1n + 12n = 13n
(4 + 13n + 3n2) = 0

Solving
4 + 13n + 3n2 = 0

Solving for variable 'n'.

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

Subproblem 1
Set the factor '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

Add '-4' to each side of the equation.
4 + -4 + n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + n = 0 + -4
n = 0 + -4

Combine like terms: 0 + -4 = -4
n = -4

Simplifying
n = -4
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 = {-4, -0.3333333333}