The scientific principle you're referring to here is the law of conservation of mass. The unbalanced equation would be:
C5H12 + O2 --> H2O + CO2
We need the same number of each atom on both sides for mass to be conserved. Start with C because it only appears once on both sides. We have 5 on the left, so we need 5 on the right:
C5H12 + O2 --> H2O + 5CO2
Now we can do the same with H. There are 12 on the left, but only 2 on the right:
C5H12 + O2 --> 6H2O + 5CO2
Finally we can balance the O's. There are 2 on the left, but 16 on the right. Your final balanced equation will be:
C5H12 + 8O2 --> 6H2O + 5CO2
