3n^2+14n+11=0

Solution for 3n^2+14n+11=0 equation:

Simplifying
3n2 + 14n + 11 = 0

Reorder the terms:
11 + 14n + 3n2 = 0

Solving
11 + 14n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(11 + 3n)(1 + n) = 0

Subproblem 1
Set the factor '(11 + 3n)' equal to zero and attempt to solve:

Simplifying
11 + 3n = 0

Solving
11 + 3n = 0

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

Add '-11' to each side of the equation.
11 + -11 + 3n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 3n = 0 + -11
3n = 0 + -11

Combine like terms: 0 + -11 = -11
3n = -11

Divide each side by '3'.
n = -3.666666667

Simplifying
n = -3.666666667
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 = {-3.666666667, -1}