\(2^{x-3}-3.2^x=-92\)
\(\Leftrightarrow2^{x-3}\left(1-3.2^3\right)=-92\)
\(\Leftrightarrow2^{x-3}.\left(1-24\right)=-92\)
\(\Leftrightarrow2^{x-3}.\left(-23\right)=-92\)
\(\Leftrightarrow2^{x-3}=4\)
\(\Leftrightarrow2^{x-3}=2^2\)
\(\Leftrightarrow x-3=2\)
\(\Leftrightarrow x=5\)