5n^2+23n+24=0

Solution for 5n^2+23n+24=0 equation:

Simplifying
5n2 + 23n + 24 = 0

Reorder the terms:
24 + 23n + 5n2 = 0

Solving
24 + 23n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(3 + n)(8 + 5n) = 0

Subproblem 1
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

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

Add '-3' to each side of the equation.
3 + -3 + n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + n = 0 + -3
n = 0 + -3

Combine like terms: 0 + -3 = -3
n = -3

Simplifying
n = -3
Subproblem 2
Set the factor '(8 + 5n)' equal to zero and attempt to solve:

Simplifying
8 + 5n = 0

Solving
8 + 5n = 0

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

Add '-8' to each side of the equation.
8 + -8 + 5n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5n = 0 + -8
5n = 0 + -8

Combine like terms: 0 + -8 = -8
5n = -8

Divide each side by '5'.
n = -1.6

Simplifying
n = -1.6
Solution
n = {-3, -1.6}