n^2-10n+22=6

Solution for n^2-10n+22=6 equation:

Simplifying
n2 + -10n + 22 = 6

Reorder the terms:
22 + -10n + n2 = 6

Solving
22 + -10n + n2 = 6

Solving for variable 'n'.

Reorder the terms:
22 + -6 + -10n + n2 = 6 + -6

Combine like terms: 22 + -6 = 16
16 + -10n + n2 = 6 + -6

Combine like terms: 6 + -6 = 0
16 + -10n + n2 = 0

Factor a trinomial.
(2 + -1n)(8 + -1n) = 0

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

Simplifying
2 + -1n = 0

Solving
2 + -1n = 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 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1n = 0

Solving
8 + -1n = 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 + -1n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1n = 0 + -8
-1n = 0 + -8

Combine like terms: 0 + -8 = -8
-1n = -8

Divide each side by '-1'.
n = 8

Simplifying
n = 8
Solution
n = {2, 8}