What is Brutus's soliloquy about?
I presume you are referring to Brutus's long soliloquy in Act 2, Scene 1, of Julius Caesar, beginning with the words "It must be by his death." The lines are numbered 10 through 34 in my paperback edition. Brutus is trying to decide whether to take part in the conspiracy to assassinate Caesar and how to justify the action to the Roman public and the senators afterward. Evidently Brutus has nearly decided that he will indeed join Cassius and the others. He tells himself: "I know of no personal cause to spurn at him / But for the general." In other words, he has nothing to gain and has no grudge against Caesar but is only concerned about the welfare of the Roman people and the future of the Republic. His most important point relates to the sentence, "He would be crowned." Brutus takes this as a positive fact. He tells himself that Caesar seems harmless enough at present but probably would become a dangerous tyrant. "And therefore think him as a serpent's egg, / Which, hatched, would as his kind grow mischievous, / And kill him in the shell." Among other things, this shows Brutus as a noble Roman. At the very end of the play, Antony says of the dead Brutus: "This was the noblest Roman of them all. / All the conspirators save only he / Did that they did in envy of great Caesar. / He only in a general honest thought / And common good to all made one of them." (5.5.67-71)