"Barracks emperors" were generals who seized power for a short period of time and then died violently.

Rome was so large it became too hard to govern.

To solve this issue, Rome divided into the eastern and western halves. This split only caused more issues with the co-emperors and the generals that rule each half fighting for control.

When external conflicts hit Rome, there weren't enough resources and people to fight because of the decline in the economy and population.

Germanic people (Visigoths were the major kind) migrated to the eastern and northern borders of the Roman Empire. They adopted the customs of the Roman Empire and even gave soldiers to the Roman Empire but the Roman Empire wouldn't allow them to become citizens so that the nomadic people could act like buffer states.

When the Huns invaded the Visigoths area, the Germanic people fled to the Roman Empire.
When the Germanic people were inside the Roman Empire, they met little residence and established settlements in the western side of the empire.

The Visigoths invaded Rome and sacked it. The western half of the empire disintegrated.