Writing a simple equation parser

Question

What sorts of algorithms would be used to do this (as in, this is a string, and I want to find the answer):

((5 + (3 + (7 * 2))) - (8 * 9)) / 72

Answer 1

Or you can just do this in one line in R:

> eval(parse(text = '((5 + (3 + (7*2))) - (8 * 9))/72' ))
[1] -0.6944444