Explain how sodium carbonate can be used to soften hard water

Hard water has Calcium and magnesium ions dissolved.
When you add sodium carbonate, calcium and magnesium precipates out as the carbonates, and "soft" water then flow. Whatever cations were belonging to the original calcium/magnesium ions, will attach to the sodium ions (and become soluble (sodium compounds are very dissolvable).
So washing soda (Sodium carbonate) is a common ingredient in washing powders because of this.
Curiously, citric acid also softens water, I add about 1/3 C per tank when adding Potassium Chloride. Think about how citric acid softens water.
I am so generous...check on the solubility of acetate compounds here: http://www.mlbgsd.k12.pa.us/cms/lib/PA09000085/Centricity/Domain/83/SOLUBILITY%20RULES.pdf

I need an ionic equation

Studient

NaCO3 +Ca2+---------- Na+ + CaCO3

YES

lol