5n^2+22n+24=0

Solution for 5n^2+22n+24=0 equation:

Simplifying
5n2 + 22n + 24 = 0

Reorder the terms:
24 + 22n + 5n2 = 0

Solving
24 + 22n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(12 + 5n)(2 + n) = 0

Subproblem 1
Set the factor '(12 + 5n)' equal to zero and attempt to solve:

Simplifying
12 + 5n = 0

Solving
12 + 5n = 0

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

Add '-12' to each side of the equation.
12 + -12 + 5n = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 5n = 0 + -12
5n = 0 + -12

Combine like terms: 0 + -12 = -12
5n = -12

Divide each side by '5'.
n = -2.4

Simplifying
n = -2.4
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 = {-2.4, -2}