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solve x*exp(x)==0 and x*exp(-x)==0

sage: solve(x*exp(x)==0,x) [x == 0, e^x == 0]

but

sage: solve(x*exp(-x)==0,x) [x == 0]

How can i avoid the e^x==0 in the solutionlist?

Thanks for help.

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No.2 Revision

solve x*exp(x)==0 and x*exp(-x)==0

sage: solve(x*exp(x)==0,x)
[x == 0, e^x == 0]

0]

but

sage: solve(x*exp(-x)==0,x)
[x == 0]

0]

How can i avoid the e^x==0 in the solutionlist?

Thanks for help.