I want to use PHP to calculate simple algebraic expressions like, 8*(5+1), entered via an <input> tag by a normal user (which means, normal notation: no syntax changes like Multiply(8, Add(5, 1))). Also, it has to show all steps, but that's not hard. The problem, right now, is calculating the value of the expressions.

Note: this is what I thought so far, which is quite inefficient but it's a provisory solution. Just replace strings where possible: in our example, recognize the string 5+1 and replace it with 6. Then, loop again, replace (6) with 6, loop again, and replace 8*6 with 48. The code for multiplying, for example, should look like this:

for ($a=1; $a < 1000; $a++) {
    for ($b=1; $b < 1000; $b++) {
        string_replace($a . '*' . $b, $a*$b, $string);
    }
}