3n^2+24n+2n+16=0

Solution for 3n^2+24n+2n+16=0 equation:

Simplifying
3n2 + 24n + 2n + 16 = 0

Reorder the terms:
16 + 24n + 2n + 3n2 = 0

Combine like terms: 24n + 2n = 26n
16 + 26n + 3n2 = 0

Solving
16 + 26n + 3n2 = 0

Solving for variable 'n'.

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

Subproblem 1
Set the factor '(8 + n)' equal to zero and attempt to solve:

Simplifying
8 + n = 0

Solving
8 + n = 0

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

Add '-8' to each side of the equation.
8 + -8 + n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + n = 0 + -8
n = 0 + -8

Combine like terms: 0 + -8 = -8
n = -8

Simplifying
n = -8
Subproblem 2
Set the factor '(2 + 3n)' equal to zero and attempt to solve:

Simplifying
2 + 3n = 0

Solving
2 + 3n = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3n = 0 + -2

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

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

Divide each side by '3'.
n = -0.6666666667

Simplifying
n = -0.6666666667
Solution
n = {-8, -0.6666666667}