`11 H_2O + 12 CO_2 -> C_1_2H_2_2O_1_1 + 12 O_2`
Here are the steps to balancing this equation:
Hydrogen: Multiplying `H_2O` by 11 gives 22 H's on each side.
Oxygen: Skip this for now
Carbon: Multiplying `CO_2` by 12 gives 12 C's on each side.
Now balance oxygen: Multiplying `O_2` by 12 gives 35 O's on each side.
Go in order from left to right, counting the number of atoms on each side and adding whole-number coefficients as needed to make both sides equal.
Save free elements for last, as was done here with oxygen. They can be balanced without changing the number of atoms of any other element.
Always double check each each element after balancing.
A hint for some equations that wasn't needed here: If there's an odd number of an element on one side and an even number on the other side, which often happens with `O_2` , multiply everything by 2 then resume balancing.