Neighbouring planets will join the revolt as the event goes on. To the best of my knowledge though, the only one you need to particularly worry about tackling is the original troublemaker.

Next time, just land a healthy amount of troops on the troublesome planet, and either give out some goods, or institute a crackdown, and the revolt should cease. Planetary leaders can help too, as can some buildings.

Originally posted by Sam:

Neighbouring planets will join the revolt as the event goes on. To the best of my knowledge though, the only one you need to particularly worry about tackling is the original troublemaker.

Next time, just land a healthy amount of troops on the troublesome planet, and either give out some goods, or institute a crackdown, and the revolt should cease. Planetary leaders can help too, as can some buildings.

I had over 30 troops on there but it was 10.5 and there was nothing I could do

Funny thing about rebels, they tend not to stick to easily-controlled locations and spread out like cockroaches on cocaine; and they definitely don't play fair, because that would be bloody stupid of them to do.

What exactly was the cause of the instability on the main rebellious world anyway? Crime? General unhappiness? A psionic backlash? Overpopulation? Some combination of these? Any and all problems of this kind can be resolved in certain ways, but we can only offer general advice with the information we have.

always watch your stability on planets
better keep it above 50 and no one will get hurt

see more info here
https://stellaris.paradoxwikis.com/Situations#Planetary_Revolt

Originally posted by Richard:

I had over 30 troops on there but it was 10.5 and there was nothing I could do

Revolts can always be prevented if you're prepared. If you realize you conquered a planet that you can't make happy through resettlement or increasing amenities, you can simply begin building fortresses immediately and use the crackdown option in the situation, and assign a high level admiral for the extra army strength to slow down/reverse the situation.

If you don't understand the exact mechanics involved, see:
https://stellaris.paradoxwikis.com/Situations#Planetary_Revolt

Stellaris in a nutshell: Slowly build up your empire and scrap the save and try again.

Stuff I've learned: Empire Size from pops is the most important end-game priority. Otherwise it takes like 100-200k science for a single tech.

Envoys are pretty OP for turning a belligerent CIV into a friendly one. I've currently got 5 envoys improving relations with one CIV. They WILL be my ally instead of getting into early wars.

You don't need the strongest fleet. The game heavily favors playing diplomacy (Vassals, Federations, etc.)

I sent my 10% Habitability Pops to a Tomb World to see if they will self-modify. I will keep the planet very low pop until they do. Fun Times.

Early game rush chokepoints and close borders to secure territory. Its a bit like playing the boardgame Risk in that regard. Scout the chokepoints early. Remember that trade networks and sectors tend to be about 4 hops. I tend to create vassals once I develop more than 3 sectors.

Originally posted by Whispdragoon62:

Empire Size from pops is the most important end-game priority. Otherwise it takes like 100-200k science for a single tech.

I'm not sure I'd call it the MOST, but I too learned how powerful small empire size is not only for tech but also for Traditions/Perks. You burn through them. Small empire size is the equivalent of many thousands of research or unity points per month, but without buildings, jobs, expense, etc. I never realized that until I tried a "tall" empire for the first time.