Here's the balanced chemical equation:

2 Fe + 3 Br₂ → 2 FeBr₃

Let me break down why:

* Iron is a transition metal, meaning it can form multiple oxidation states. In this case, it forms the +3 oxidation state.

* Bromine is a nonmetal and forms a -1 anion (Br⁻).

To balance the charges and form a neutral compound, we need three bromide ions (3Br⁻) for every iron ion (Fe³⁺).