Is it possible to lose weight and build muscles at the same time?

I'm 175 cm and 80 kg , was 90 kg 6 months before and lost 10 kg by changing my diet and dancing and playing kinect's games.
Now I want to start going gym and thinking of build some muscles and lose fat together. Is it possible?
If I try hard can I reach an ideal shape in the next 6 months?
Updates
+1 y
Forgot to say that I don't want huge muscles and bulky looks just lean muscles and be in shape.
Is it possible to lose weight and build muscles at the same time?
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