Help with writing a balanced equation to show how ions can be removed by using sodium carbonate?

2Fe³⁺(aq) + 3CO₃²⁻(aq) → Fe₂(CO₃)₃(s)

Iron ions ....

There are not likely to be high concentrations of iron(III) ions in drinking water. They will react with oxygen to form Fe2O3(s) or Fe(OH)3(s). On the other hand Fe(II) ions may be found in drinking water. If there are high concentrations of iron expect to see suspended particles which make the water yellowish or reddish brown.

And even if there were Fe3+ ions present, they will not combine with carbonate ion to make hypothetical "iron(III) carbonate." Fe2(CO3)3 does not exist. Iron(III) is too acidic to form a stable carbonate. Iron(III) ions undergo hydrolysis (reaction with water) and produced hydrogen ions.
.... Fe3+ + HOH --> Fe(OH)^2+ + H+
.... Fe3+ + 2HOH --> Fe(OH)2^+ + 2H+
.... Fe3+ + 3HOH --> Fe(OH)3(s) + 3H+

If Fe3+ and CO3^2- are combined, CO2 gas will be given off and Fe2O3(s) will precipitate.
..... 2Fe3+ + 3CO3^2- --> Fe2O3(s) + 3CO2(g)

You can precipitate iron(III) ions by adding carbonate, and making Fe2O3(s), but don't expect to see Fe2(CO3)3 as the insoluble product.