How to find the equilibrium points and stability of a system of two diff. equations

Question

I'm having a hard time working this out.

My system discribes the evolution of the population of $2$ species: $$ \frac{dP}{dt} = (a - bP - kQ)P, \\ \frac{dQ}{dt} = (c - dQ - lP)Q. $$ As i understand, to find the equilibrium point i must do $P'(t) = Q'(t) = 0$, right? With this two equations i should get 4 equilibrium points. $$ (a - bP - kQ)P = 0, (c - dQ - lP)Q = 0. $$ The only way i found to work this around was:

1. if I consider $P=0$, I get $(0, \frac{c}{d})$.
2. if I consider $Q=0$, I get $(\frac{a}{b}, 0)$.
3. if I consider $P=0$ and $Q=0$, I get $(0,0)$.
4. ?

Is what i did remotely correct? If not, how do i do this?

For the stability I know I have to do the Jacobian matrix and I think I can do it once I have the $4$ equilibrium points.

Thanks in advance.