Неравенство 0.6^lg^2*(-x)+3 > (5/3)^-2lgx^2

$0,6^{lg^2(-x)+3}\ \textgreater \ ( \frac{5}{3} )^{-2lgx^2}; \\ (\frac{3}{5})^{lg^2(-x)+3}\ \textgreater \ ( \frac{3}{5} )^{2lgx^2}; \\ lg^2(-x)+3\ \textless \ 2lgx^2; \\ lg^2(-x)-4lg(-x)+3\ \textless \ 0; \\ lg(-x)=t; \\ t^2-4t+3\ \textless \ 0; \\ D=16-12=4; \\ t_{1}= \frac{4-2}{2}=1; \\ t_{2}= \frac{4+2}{2}=3. \\ 1\ \textless \ t\ \textless \ 3; \\ 1\ \textless \ lg(-x)\ \textless \ 3; \\ lg10\ \textless \ lg(-x)\ \textless \ lg1000; \\ 10\ \textless \ -x\ \textless \ 1000; \\ -1000\ \textless \ x\ \textless \ -10. \\ x\ \textless \ 0. \\$
Ответ: (-1000;-10).