Derivative to find rate of change/population.

I'm just looking for someone to point me in the right direction for this question. It's easy in theory but I'm stuck on it for some reason!

8. The fish population in a lake can be modeled by the function p(t) = 15(t^2 + 30)(t + 8), where t is time in years from now.

a) Determine the rate of change of the fish population when there are 5000 fish in the lake.

b) When will the fish population double from its current level? What is the rate of change in the fish population at this time?

So p'(t)= 45t^2 + 240t + 450

a) 0= 15t^3 + 120t^2 + 450t - 1400

b) 0= 15t^3 + 120t^2 + 450t - 3600

From there I just can't seem to factor and work out the answer. Thanks.