5n^2-22=-n

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

Simplifying
5n2 + -22 = -1n

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

Solving
-22 + 5n2 = -1n

Solving for variable 'n'.

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

Combine like terms: -1n + n = 0
-22 + n + 5n2 = 0

Factor a trinomial.
(-11 + -5n)(2 + -1n) = 0

Subproblem 1
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
Subproblem 2
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
Solution
n = {-2.2, 2}