I consider whether the equation has, or implies, some type of equation that I have come across before, or that seems to be appreciably simpler. The next step is to look for simple solutions that might give a clue as to how a general solution might be found. For this problem, those solutions are $s = 0$, $s = e^t$ and $s = -e^t$, but the given equation looks quite awkward, and I haven't made further progress yet.