To balance equations, I like to start by creating two columns: a column on the left to show simply the symbols (not the quantities) of the elements that are in the reactants, and a column on the right to show the elements in the products. Most of the time the two columns should match.
In this case we have
So the elements in each column should be Li, C and O
Then I do the appropriate math for each side to find the total number of atoms.
2 Li 4 Li
1 C 2 C
3 O 6 O
Fortunately the product is simply double the amount of the reactant all the way across, so we only have to double the number of reactant molecules to balance the equation; `2Li_(2)CO_(3) -> 2CO_(2) + 2Li_(2)O` .
The advantage to this method is that you don't have to repeatedly re-balance if balancing one atom doesn't balance the rest as well.
The first step for balancing this equation is to balance the Li. Because the right side of the equation has 4 Li we must make it so the left side also has 4 Li
2Li^2CO^3 = 2CO^2 + 2Li^2O
Everything looks balanced now but a check should be performed to ensure accuracy.
Left side: 4 Li, 2 C, 6 O
Right side: 2 C, 4 Li, 6 O