How do you simplify algebraic expressions?

There are many reasons one may want to simplify, rearranging to find specific values - or maybe just making it simpler
Well, let's do some examples:
y(x(3+2)) +2 = -2y +2   < I just made this one up, it looks really complicated right now, none the less it can be simplified easily
y(3x+2x) + 2 = - 2y +2
3xy + 2xy + 2 = -2y +2
5xy + 2 = -2y +2    <-- the +2's dissapear because they cancel out
5xy = -2y

And there we have it, that long expression has been simplified to something really simple.

Another example:
3(4(x+3(2 +z)) - 5)= 3y <- you can start where ever, I like starting in the middle
3  *  (4 *  (x +  3*(2 + z)) -  5 ) = 3y  <-  here it is spaced out, we get a much better view
3  *  (4 *  (x +  6 + 3z) -  5 ) = 3y
3  * (4x + 24 + 12z - 5) = 3y <- divide both sides by 3 ..
4x + 24 + 12z - 5 = y <- much better

Note: Simplify means solving to a degree, but you can't solve it because it has unknowns