Any number inside the modulus sign becomes positive. This means and so we have,
Solving these gives us
However if we check the second solution in the original equation we obtain . This is false and so
can't be a solution.
Therefore the only solution is .
(Note: I'm not sure why the second solution didn't work but when there's a modulus sign involved it always pays to check your final answers to be sure. I'll have a think about it but in case you find out before I do, I'd be interested to know in the comments.)