n^2+9n+22=8

Solution for n^2+9n+22=8 equation:

Simplifying
n2 + 9n + 22 = 8

Reorder the terms:
22 + 9n + n2 = 8

Solving
22 + 9n + n2 = 8

Solving for variable 'n'.

Reorder the terms:
22 + -8 + 9n + n2 = 8 + -8

Combine like terms: 22 + -8 = 14
14 + 9n + n2 = 8 + -8

Combine like terms: 8 + -8 = 0
14 + 9n + n2 = 0

Factor a trinomial.
(7 + n)(2 + n) = 0

Subproblem 1
Set the factor '(7 + n)' equal to zero and attempt to solve:

Simplifying
7 + n = 0

Solving
7 + n = 0

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

Add '-7' to each side of the equation.
7 + -7 + n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + n = 0 + -7
n = 0 + -7

Combine like terms: 0 + -7 = -7
n = -7

Simplifying
n = -7
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 = {-7, -2}