\(\frac{x-1}{27}=-\frac{3}{1-x}\)
\(\left(x-1\right)\left(1-x\right)=-27.3\)
\(\Rightarrow\orbr{\begin{cases}x=-8\\x=10\end{cases}}\)
\(\frac{x-1}{27}=\frac{-3}{1-x}\)
\(\Rightarrow\left(x-1\right).\left(1-x\right)=\left(-3\right).27\)
\(\left(x-1\right)\left(1-x\right)=-81\)
\(\Leftrightarrow x-x^2-1+x=-81\)
\(x-x^2+x=-80\)
\(\Leftrightarrow2x-x^2=-80\)
\(x\left(2-x\right)=-80\)
\(\Rightarrow\orbr{\begin{cases}x=10\\x=-8\end{cases}}\)