Lots of people have the goal of losing weight while building muscle at the same time, the question is...can you do it?
In short, yes...although it's only possible under certain conditions. We recommend you normally tackle one at a time in phases of 4-6 weeks. The reason for this is that to lose weight you often have to be in a calorie deficit (eating less calories than you burn), while gaining muscle requires a calorie surplus (eating MORE calories than you burn off). You can see that both goals therefore compete with each other.
The best way to focus in on one at a time is to be honest with yourself and think "what is more important to me first off, dropping the fat or putting on more muscle". From there you're in a better position to decide on what plan to focus on first, then what plan to work towards after.
The ability to build lean muscle and burn fat at the same time is known as body recomposition and relies entirely on very well dialled in nutrition.
To build muscle while in a calorie deficit requires protein synthesis to be very high (or protein breakdown to be very low) or a combination of both. Tackling these will allow you to work towards both goals.
So how can you do it?
Maintain a MODERATE calorie deficit
Aim for 1.2 grams of protein per lb of bodyweight per day
1 gram of carbohydrates per lb of bodyweight per day
0.2 grams of fat per lb of bodyweight per day
Do heavy compound lifts to build muscle & burn fat and keep strength
Do HiiT (1-2 hours broken up through the week)
Get enough sleep (releases growth hormone)
Use supplements to aid your training (creatine for strength, BCAA's with high Leucine content to preserve, synthesise and build muscle, L-Carnitine to drop stubborn fat & help performance and even possibly a ZMA supplement to help quality sleep & recovery).
So in summary, yes it's possible, but the reason it's too hard for most people is that the nutrition side let's them down, hence why tackling one goal of fat loss or muscle building at a time is easier. If you can get this right though and commit to the diet and training side, body recomposition is possible.