How did rome gain control of italy after the sacking of the city by the gauls?

The Gallic sack left very few marks on the city, In particular, archaeology has shown it was not burnt.

Rome didn't REgain control of Italy after the Gallic sack in 386, as she didn't have it before. The decisive date was 338 BC when Rome crushed the Latin league. The peace settlement allowed Latins a good many of the benefits of Roman citizenship, and the promise of more. In consequence Rome got stronger and had more manpower with each extension of its territory, and was supreme in Italy after beating the Etruscans and Samnites at Cominium and Aquilonia in 293 BC ...