Look at what W|A claims as its interpretation of the input. That "solve" has it trying to find where the product is zero. Sonce the product simplifies to x, you get that x=0.
x
x=0
You don't need the word "Solve", i.e. your input must be simply:
(sqrt(x^2+x) - x) (sqrt(x^2+x) + x)
and the result is x.
