5n^2+21n+22=0

Solution for 5n^2+21n+22=0 equation:

Simplifying
5n2 + 21n + 22 = 0

Reorder the terms:
22 + 21n + 5n2 = 0

Solving
22 + 21n + 5n2 = 0

Solving for variable 'n'.

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

Simplifying
2 + n = 0

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

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

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

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