#397Equation Elation

The author of an elementary school algebra text book has approached you to write a program to solve simple algebra equations. The author wants to use a program to avoid human errors in preparing the solutions manual. The text book author will provide a text file of the simple problems for your problem to solve. All of the problems will be in the form of an algebraic equality. The specific syntax of the problems will be an algebraic statement consisting of integer constants and the four basic arithmetic operators, an equal sign, and a variable. For example:

12 - 4 * 3 = x

For the solutions manual the problem is not just to be solved, but solved one step at a time. For the above input line, the corresponding output would be:

12 - 4 * 3 = x
12 - 12 = x
0 = x

The simple problems your program is to solve are limited to integer values with multiplication, division, addition and subtraction operations. Note that, as in the above example, the computation must follow the standard order of precedence for arithmetic operations. All multiplications and divisions are performed, from left to right, before any additions and subtractions, and then all additions and subtractions are performed from left to right. You may assume that all divisions will result in integer values.

3 * 4 + 4 - 1 / 1 = xyzzy
12 + 2 * 12 / 2 - 1 = y
2 * -3 + -6 - +4 = r
2*-3+-6-+4=r

3 * 4 + 4 - 1 / 1 = xyzzy
12 + 4 - 1 / 1 = xyzzy
12 + 4 - 1 = xyzzy
16 - 1 = xyzzy
15 = xyzzy

12 + 2 * 12 / 2 - 1 = y
12 + 24 / 2 - 1 = y
12 + 12 - 1 = y
24 - 1 = y
23 = y

2 * -3 + -6 - 4 = r
-6 + -6 - 4 = r
-12 - 4 = r
-16 = r

2 * -3 + -6 - 4 = r
-6 + -6 - 4 = r
-12 - 4 = r
-16 = r