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What is the balanced equation of calcium carbonate (s) > calcium oxide (s) + carbon dioxide (g)?
The equation is already balanced
In terms of molecular format the equation is written as follows:
##CaCO_3## ##rarr## ##CaO## + ##CO_2##
On the left hand side of the equation there are:
1 Calcium 1 Carbon 3 Oxygen
On the right side of the equation there are:
1 Calcium 1 + 2 = 3 Oxygen 1 Carbon
Therefore the left side equals the right side and is thus balanced.
Generally these summarized rules can be followed to balance equations:

Write the correct chemical formulas for all of the reactants and the products.

Write the formulae of the reactants on the LEFT of the reaction arrow; write the formulas of the products on the RIGHT of the reaction arrow.

Count the total number of atoms/ions of each element in the reactants and the total number of atoms/ions of each element in the products.

Balance the elements one at a time using coefficients. A coefficient is a small whole number that is written in front of a chemical formula in a chemical equation.
It is best to begin with elements other than hydrogen and oxygen! These elements often occur more than twice in equations.

Check each atom/ion, or polyatomic ion to be sure that the equation is correctly balanced.

Finally, make sure that all of the coefficients are in the lowest possible whole number ratios.
*Unsummarized rules for balancing found at: https://www.greenwichschools.org/uploaded/faculty/arleene_ferko/Unit_8_Notes_7_RULES_FOR_BALANCING_CHEMICAL_EQUATIONS.doc
Hope I helped :)