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OK first off you can't lose fat and gain muscle at the same time, it's almost metabolically impossible, so doing cardio then straight after doing weight training or vice versa is pointless and counter productive.
The best way to lose weight is to do 15 minutes of high intensity interval cardio training 3-5 times a week with a focus of continually increasing the intensity each time, while eating slightly less than you normally do.
This will increase your resting metabolism rate so you can burn fat while lazing around or whatever (you almost never actually burn a significant amount of fat while doing cardio itself).
Or you could do some weight training which will increase your resting metabolism rate as you gain muscle, however in order to gain muscle you'll have to eat more which will inevitably lead to fat gain.
Fat loss necessitates a deficiency of calories while muscle gain necessitates a surplus of calories.
So it depends on which one you want first; fat loss or muscle gain.[/i]
this post is almost dead on. good job charlie
from your particular situation though, it is entirely possible to gain muscle while losing fat. i can go into the science of this if you'd like, but simply put, just split your time at the gym. any time you are lifting weights that challenge your body, you will breakdown muscle, and let it rebuild itself. also, any time you are doing HIT (high intensity cardio. [any cardio that you dont normally do durring the day. so jogging, walking uphill on the machine, doing a high pace stride on an eliptical machine] ) you will be burning calories, thus dropping your body fat. so short answer is yes you can drop body fat while gaining muscle initially, but as you progress it will be harder to do both at the same time because of the reasons listed by charlie.
no matter what is happening though, going and working out is never a bad thing and can only serve to better you, thus raising your confidence and helping your pickup!