3n^2+22n+32=0

Solution for 3n^2+22n+32=0 equation:

Simplifying
3n2 + 22n + 32 = 0

Reorder the terms:
32 + 22n + 3n2 = 0

Solving
32 + 22n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(16 + 3n)(2 + n) = 0

Subproblem 1
Set the factor '(16 + 3n)' equal to zero and attempt to solve:

Simplifying
16 + 3n = 0

Solving
16 + 3n = 0

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

Add '-16' to each side of the equation.
16 + -16 + 3n = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 3n = 0 + -16
3n = 0 + -16

Combine like terms: 0 + -16 = -16
3n = -16

Divide each side by '3'.
n = -5.333333333

Simplifying
n = -5.333333333
Subproblem 2
Set the factor '(2 + n)' equal to zero and attempt to solve:

Simplifying
2 + n = 0

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

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

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

Simplifying
n = -2
Solution
n = {-5.333333333, -2}