My assignment is to determine fixed points of the differential equation
$$\frac{dN}{dt} = \left(\frac{aN}{(1+N)} - b -cN\right)N$$ where $a,b,c > 0$ and find out their stability.
I do understand that concerning differential equations, a fixed point is defined as the $N$ which solves the equation $N = f(N) \cdot N$. For some reason I cant even start since I only get rubbish when trying to solve for $N$ from the equation. Any suggestions where to start?