How do you expand out and simply brackets, like the following: (x-3)(x+4)?

So when you want to expand out 2 brackets, there's a really simple method, known as FOIL. FOIL stands for "First, Outer, Inner, & Last". So if we look at the two brackets you gave as an example, imagine that we've separated them into 4 blocks: x, -3, x, and 4. The first thing we do is look at the first numbers in each bracket, which would be x, and x. We multiply those together, giving you x². Then we move onto the next step of FOIL, which is Outer. As the outer values in this case are x, and 4, you multiply those and get 4x. It's the same with the step 3, Inner. This time we'll take the -3 and times it with the x, giving you -3x. Finally, you multiply the last numbers of each bracket. What would that give you? So -3*4 would be -12. That's how you expand the brackets!The next step is to simply the brackets, which can be quite satisfying, because all the pieces fall together into a nice equation. You have the x², the 4x, the -3x, and the -12. You want to add all of these together, giving you: x²+4x-3x-12.If you look at the two middle values, you can see that the 4x and -3x can actually be simplified together, into +x, meaning the complete simplified equation would be: x²+x-12!