For the record, in 99% of driving scenarios, you probably don't want to press the brake and gas at the same time. For the 1%, you can do something called brake boosting. This is where on turbo cars, you brake to maintain a slower speed, at the same time you press the gas to spool up the turbo, which results in you having little to no turbo lag while racing.

Similar technique would be used for manuals as well. You'd heal-toe on a hill so you don't roll back, same with downshifting and slowing down quickly to make a turn.