Given an equation to solve for n:

The expansion of the given sum is as follows:

Now, factorise the above quadratic equation:

Use zero product rule in the equation to get:
5n + 83 = 0 or n - 24 = 0 which implies n = -83/5 and n = 24.
Neglect the negative solution of the equation to get n = 24.
Thus, the answer is 24.