I do not understand what this is asking me to do. I've several different ways and I do not feel comfortable with my answer.
n^3 -5n^2 -2n +24 =0
Any guidance would be so helpful
I think they want you to discover or calculate which values of n satisfy the equation.
For instance, n=0 will not work, because then the expression = 24
The fact that cubics are hard to solve in general, yet they are asking you to solve this one, indicates to me that you must have studied things like the Remainder Theorem and the Rational Roots Theorem and synthetic division.
You should be able to tell that any rational roots are factors of 24.
Knowing that, start checking the easy values using synthetic division to discover that n = -2 is a root, so you can factor out (x+2) giving you
(n+2)(n^2-7n+12)
then you can use the quadratic formula or inspection to get the final factored form
(n+2)(n-3)(n-4) = 0
Now you know that if the product of numbers is zero, at least one of the numbers must be zero. This means that
n = -2 or 3 or 4