5n^2+2n-24=0

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

Simplifying
5n2 + 2n + -24 = 0

Reorder the terms:
-24 + 2n + 5n2 = 0

Solving
-24 + 2n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-12 + -5n)(2 + -1n) = 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 + -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 = {-2.4, 2}