3n^2+11n+14=6

Solution for 3n^2+11n+14=6 equation:

Simplifying
3n2 + 11n + 14 = 6

Reorder the terms:
14 + 11n + 3n2 = 6

Solving
14 + 11n + 3n2 = 6

Solving for variable 'n'.

Reorder the terms:
14 + -6 + 11n + 3n2 = 6 + -6

Combine like terms: 14 + -6 = 8
8 + 11n + 3n2 = 6 + -6

Combine like terms: 6 + -6 = 0
8 + 11n + 3n2 = 0

Factor a trinomial.
(8 + 3n)(1 + n) = 0

Subproblem 1
Set the factor '(8 + 3n)' equal to zero and attempt to solve:

Simplifying
8 + 3n = 0

Solving
8 + 3n = 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 + 3n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3n = 0 + -8
3n = 0 + -8

Combine like terms: 0 + -8 = -8
3n = -8

Divide each side by '3'.
n = -2.666666667

Simplifying
n = -2.666666667
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 = {-2.666666667, -1}