Where Did I Go Wrong Balancing This Single Displacement Reaction?

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Homework Statement


This is a single displacement reaction
aluminum + hydrochloric acid -->


Homework Equations





The Attempt at a Solution


Since I know its single displacement, and I know that aluminum can't trade places with chlorine because one is a metal and one is a non-metal, aluminum must trade places with hydrogen, which I know can trade places with a metal.

Al + HCl --> H + AlCl

Since I know that hydrogen is a diatomic element, I must change it to H2

Al + HCl --> H2 + AlCl

Now it's out of balance because there are 2 hydrogens on the right. So I balance it by multiplying the left HCl by 2.

Al + 2HCl --> H2 + AlCl

This leaves Cl out of balance, so I multiply the right one by 2.

Al + 2HCl --> H2 + 2AlCl

This leaves Al out of balance, so I multiply the left one by 2.

2Al + 2HCl --> H2 + 2AlCl

Seems to be balanced now. But when I look up the answer by Googling, I find that I should have ended up with
2Al + 6HCl --> 2AlCl3 + 3H2

Where did I go wrong? Thanks!
 
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