Your calculations are not correct as far as I can see, it's hard to follow where you have go the first equation.
You should follow a process as such:
- Start by labelling all nodes. There are 6 output nodes by my count, including the output Q.
- Write down the each equation of each node in relation to the nodes before it. You will end up with 6 equations in this case.
- Substitute in prior equations to build up a final non-simplified equation for Q.
- Simplify using Boolean algebra rules.
I'll give you a hint, in this particular example you will end up with a very simple equation that is well grounded.