Brute forcing is not a technique, it is more like a state of mind. Normally you are “with the numbers” when you are calculating; you know where you are in the calculation, where you were before and where you are next. Brute forcing is like letting your calculating mind run ahead of you and you just have to quickly catch the numbers that it throws at you. With brute forcing you just have to trust your gut, or in this case, your brain that it spews out the right numbers.
All of us look sometimes at a calculation twice or check the steps again, even though your first calculation is probably right. Next time, try to calculate something and as soon as you have an in-between answer, force yourself to the next step in the calculation, no looking back, trust your brain.
When I do calculations, it is not a matter of “if” but often a matter of “when” I can get the answer. So, I tried to shorten the “when” part by removing the thing that slows me down the most, myself, and it works. I used to call it “turbo-mode” when I was younger but brute forcing sounds better, haha:)