n^2+14n+41=8

Solution for n^2+14n+41=8 equation:

Simplifying
n2 + 14n + 41 = 8

Reorder the terms:
41 + 14n + n2 = 8

Solving
41 + 14n + n2 = 8

Solving for variable 'n'.

Reorder the terms:
41 + -8 + 14n + n2 = 8 + -8

Combine like terms: 41 + -8 = 33
33 + 14n + n2 = 8 + -8

Combine like terms: 8 + -8 = 0
33 + 14n + n2 = 0

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

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

Simplifying
11 + n = 0

Solving
11 + n = 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 + n = 0 + -11

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

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

Simplifying
n = -11
Subproblem 2
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

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

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

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

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

Simplifying
n = -3
Solution
n = {-11, -3}