5n^2-n-22=0

Solution for 5n^2-n-22=0 equation:

Simplifying
5n2 + -1n + -22 = 0

Reorder the terms:
-22 + -1n + 5n2 = 0

Solving
-22 + -1n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-2 + -1n)(11 + -5n) = 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 '(11 + -5n)' equal to zero and attempt to solve:

Simplifying
11 + -5n = 0

Solving
11 + -5n = 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 + -5n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -5n = 0 + -11
-5n = 0 + -11

Combine like terms: 0 + -11 = -11
-5n = -11

Divide each side by '-5'.
n = 2.2

Simplifying
n = 2.2
Solution
n = {-2, 2.2}