n^2+22=10n-2

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

Simplifying
n2 + 22 = 10n + -2

Reorder the terms:
22 + n2 = 10n + -2

Reorder the terms:
22 + n2 = -2 + 10n

Solving
22 + n2 = -2 + 10n

Solving for variable 'n'.

Reorder the terms:
22 + 2 + -10n + n2 = -2 + 10n + 2 + -10n

Combine like terms: 22 + 2 = 24
24 + -10n + n2 = -2 + 10n + 2 + -10n

Reorder the terms:
24 + -10n + n2 = -2 + 2 + 10n + -10n

Combine like terms: -2 + 2 = 0
24 + -10n + n2 = 0 + 10n + -10n
24 + -10n + n2 = 10n + -10n

Combine like terms: 10n + -10n = 0
24 + -10n + n2 = 0

Factor a trinomial.
(4 + -1n)(6 + -1n) = 0

Subproblem 1
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {4, 6}