Balancing is usually alot of guesses to get where you are.
H2O2+N2H4->HNO3+H2O
How I did this problem was by seeing how many moles of a certain element are there.
Original: H2O2+N2H4->HNO3+H2O
H 2 4 1 2 Unequal! 6 versus 3
O 2 3 1 Unequal! 2 versus 4
N 2 1 Unequal! 2 versus 1
7H2O2+N2H4->2HNO3+8H2O is your final answer (alot of guessing!)
