calculus - Logistic differential equation problem

I'm taking the AP Calculus BC Exam next week and ran into this problem with no idea how to solve it. Unfortunately, the answer key didn't provide any explanations.

I'm having trouble turning the differential equation into a normal equation. A step-by-step explanation would be wonderful.

The population P(t) of a species satisfies the logistic differential equation dP/dt = P(224 - (P^2)/56) where the initial population P(0) = 30 and t is the time in years. What is the limit of P(t) as t approaches infinity? (Calculator allowed)

Answer

Given that the population has a logistic form, at long times (large t), the population reaches a steady state. Thus $dP/dt = 0$ as t approaches infinity.

Solving for P yields $\pm 112$