When do I use "brauchen + zu + Infinitiv" vs. "müssen"?
müssen: Strong obligation, necessity ("must," "have to").
brauchen + zu + Infinitiv: "To need to do something." Used mostly in negative sentences ("nicht brauchen zu") to mean "not have to."
Example
Ich muss heute arbeiten. (I have to work today - strong obligation.)
Du brauchst nicht zu kommen. (You don't need to come / You don't have to come.)