n^2+27n+182=0

Solution for n^2+27n+182=0 equation:

Simplifying
n2 + 27n + 182 = 0

Reorder the terms:
182 + 27n + n2 = 0

Solving
182 + 27n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(14 + n)(13 + n) = 0

Subproblem 1
Set the factor '(14 + n)' equal to zero and attempt to solve:

Simplifying
14 + n = 0

Solving
14 + n = 0

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

Add '-14' to each side of the equation.
14 + -14 + n = 0 + -14

Combine like terms: 14 + -14 = 0
0 + n = 0 + -14
n = 0 + -14

Combine like terms: 0 + -14 = -14
n = -14

Simplifying
n = -14
Subproblem 2
Set the factor '(13 + n)' equal to zero and attempt to solve:

Simplifying
13 + n = 0

Solving
13 + n = 0

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

Add '-13' to each side of the equation.
13 + -13 + n = 0 + -13

Combine like terms: 13 + -13 = 0
0 + n = 0 + -13
n = 0 + -13

Combine like terms: 0 + -13 = -13
n = -13

Simplifying
n = -13
Solution
n = {-14, -13}