The way I was going about this originally was as follows:
Let the equation be
Pb(NO3)2 —> PbO + 2NO2 + aO2
In which case, the total number of oxygens on the RHS is given by the number of oxygens in 1 PbO + number of oxygens in 2 NO2’s + number of oxygens in a O2’s:
= (1 x 1) + (2 x 2) + (a x 2)
= 5 + 2a
Since there are 6 oxygens on the LHS and the numbers of oxygens on both sides must be the same, 5 + 2a = 6
This leads to a = 0.5, so:
Pb(NO3)2 —> PbO + 2NO2 + 0.5O2
Which can be doubled to get rid of the 0.5:
2Pb(NO3)2 —> 2PbO + 4NO2 + O2