What's the meaning of this sentence?
They succeeded each other with terrifying rapidity, murdering their way into the palace and being murdered out of it as soon as their successors had become rich enough to bribe the guards into a new rebellion.

P.S. What's the meaning of "murder one's way into ..." and "murder out of ... " in the sentence?

Question

What's the meaning of this sentence?
They succeeded each other with terrifying rapidity, murdering their way into the palace and being murdered out of it as soon as their successors had become rich enough to bribe the guards into a new rebellion.

P.S. What's the meaning of "murder one's way into ..." and "murder out of ... " in the sentence?

Answer

Murdering their way into the palace > those who want to be the rulers have to kill all those that block their claim to the throne (which is in the palace ) >To kill/murder anyone who stands in his way to power
Being murdered out of it >  To be rejected or displaced from the throne by murder of those currently sitting on the throne > being murdered * out of his throne*

Answer

It would mean in order for them to have become the rulers of the palace they killed the previous rulers. However, once they gained power, they were  in turn also killed in a rebellion. Their deaths made it possible for another to become the ruler.

I hope that helps :)