\(\frac{7-x}{2}+\frac{2}{3}.\left(x-7\right)\left(x-3\right)=0\)
\(\Leftrightarrow\frac{x-7}{-2}+\frac{2\left(x-7\right)}{3}\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-7\right)\left[\frac{-1}{2}+\frac{2}{3}\left(x-3\right)\right]=0\)
\(\Leftrightarrow\left(x-7\right)\left(\frac{-1}{2}+\frac{2x}{3}-2\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-7=0\\\frac{-1}{2}+\frac{2x}{3}-2=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=7\\-\frac{5}{2}+\frac{2x}{3}=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=7\\\frac{2x}{3}=\frac{5}{2}\end{cases}\Leftrightarrow\orbr{\begin{cases}x=7\\x=\frac{15}{4}\end{cases}}}\)
