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This is a bug (?) in to_poly_solve in Maxima.

(%i1) load(to_poly_solver);

Loading maxima-grobner $Revision: 1.6 $ $Date: 2009-06-02 07:49:49 $
(%o1) /Applications/MathApps/Sage-5.4.1-OSX-64bit-10.6.app/Contents/Resources/\
sage/local/share/maxima/5.26.0/share/contrib/to_poly_solver.mac
(%i3) display2d:false;

(%o3) false
(%i4) to_poly_solve([2*(x-1)*%e^(t*x)+t*(x-1)^2*%e^(t*x)=0,4*t*(x-1)*%e^(t*x)+t^2*(x-1)^2*%e^(t*x)+2*%e^(t*x)>0],[x]);

(%o4) %union([x = 1,2 > 0],[x = (t-2)/t,
                            t^2-2*(t-2)*t-4*t+4*(t-2)+(t-2)^2+2 > 0])

The current Maxima has

(%o4) %union([x = 1,2 > 0],[x = (t-2)/t,
                        t^2-2*(t-2)*t-4*t+4*(t-2)+(t-2)^2+2 > 0])

which is basically the same issue. I've reported this upstream here.