n^2-8n+22=7

Solution for n^2-8n+22=7 equation:

Simplifying
n2 + -8n + 22 = 7

Reorder the terms:
22 + -8n + n2 = 7

Solving
22 + -8n + n2 = 7

Solving for variable 'n'.

Reorder the terms:
22 + -7 + -8n + n2 = 7 + -7

Combine like terms: 22 + -7 = 15
15 + -8n + n2 = 7 + -7

Combine like terms: 7 + -7 = 0
15 + -8n + n2 = 0

Factor a trinomial.
(3 + -1n)(5 + -1n) = 0

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

Simplifying
3 + -1n = 0

Solving
3 + -1n = 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 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {3, 5}