Math magic

[Guest]

Add 18 to the month they were born
Multiply by 25
Subtract 333
Multiply by 8
Subtract 554
Divide by 2
Add their birth date
Multiply by 5
Add 692
Multiply by 20
Add only the last two digits of their birth year
Subtract 32940 to get their birthday!

I need to understand why this works. A break.Can someone help?

[Guest]

[tex]((((( m+18) \cdot 25-333) \cdot8-554):2+d) \cdot5+692) \cdot20+y -32940=[/tex]

[tex](((( m \cdot 25+18 \cdot 25-333) \cdot8-554):2+d) \cdot5+692) \cdot20+y -32940=[/tex]

[tex]((((25m+450 -333) \cdot8-554):2+d) \cdot5+692) \cdot20+y -32940=[/tex]

[tex]((((25m+117) \cdot8-554):2+d) \cdot5+692) \cdot20+y -32940=[/tex]

[tex](((25m\cdot8+117 \cdot8-554):2+d) \cdot5+692) \cdot20+y -32940=[/tex]

[tex](((200m+936-554):2+d) \cdot5+692) \cdot20+y -32940=[/tex]

[tex](((200m+382):2+d) \cdot5+692) \cdot20+y -32940=[/tex]

[tex]((200m:2+382:2+d) \cdot5+692) \cdot20+y -32940=[/tex]

[tex]((100m+191+d) \cdot5+692) \cdot20+y -32940=[/tex]

[tex]((100m+d+191) \cdot5+692) \cdot20+y -32940=[/tex]

[tex](100m \cdot5+d \cdot5+191 \cdot5+692) \cdot20+y -32940=[/tex]

[tex](500m+5d+955+692) \cdot20+y -32940=[/tex]

[tex](500m+5d+1647) \cdot20+y -32940=[/tex]

[tex]500m\cdot20+5d\cdot20+1647 \cdot20+y -32940=[/tex]

[tex]10000m+100d+32940+y -32940=[/tex]

[tex]10000m+100d + y + 32940 -32940=[/tex]

[tex]10000m+100d+y[/tex]