PEMDAS and Like Terms

It's these little things that always get me. I'm working on writing a program for doing expressions... but... how do I handle combining like terms and distributing? As in I'm asking if I have the right order. :3

For example, with the expression:
(5x(12x -2x + 4) + 3 + 3x - (6x -2))/2

Nice and complicated, I guess. But at what stage would I combine like terms, and also, when would you distribute? Before or after combining...

Would I just follow PEMDAS in the combining of terms? Like distribute first because it's multiplication? And do this before trying to simplify?

So:
(5x(12x -2x + 4) + 3 + 3x - (6x -2))/2
(50x+ 7 + 3x -6x+2))/2 <<<--- Distribute, combine, distribute...
(47x+ 9)/2 <<<---Combine some more...
then distribute(if that's the right word for division)
23.5x + 4.5

Would that be the right answer? I hope I wasn't too confusing.

(BTW, this isn't homework, but I assume anyone in this forum would probably be the most knowledgeable on this. )

If there are like terms within parentheses, combining them first is easiest. You can save combining like terms until the very end, but this winds up making the problem more complex, which makes the problem take longer to solve while also increasing the chances of making a mistake (if you're working it out by hand).

I've also found that it's generally a good idea to simplify/combine like terms after each PEMDAS operation. It helps cut down on mistakes.

So, for this:

(5x(12x -2x + 4) + 3 + 3x - (6x -2))/2

I'd combine the like terms in parentheses where possible, then distribute to get this:

(50x^2 + 20x +3 + 3x - 6x + 2)/2

Combining like terms again gets this:

(50x^2 + 17x + 5)/2

or

25x^2 + 8.5x + 2.5

A computer program should have no problem following through PEMDAS without simplifying after each step, though.