a)\(2007x\left(x-\frac{2006}{7}\right)=0\)
\(\Rightarrow x\left(x-\frac{2006}{7}\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x-\frac{2006}{7}=0\end{cases}}\)
\(\Rightarrow x=\orbr{\begin{cases}0\\\frac{2006}{7}\end{cases}}\)
b) \(5.\left(x-2\right)+3x\left(2-x\right)=0\)
\(=5\left(x-2\right)-3x\left(x-2\right)=0\)
\(=\left(x-2\right)\left(5-3x\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-2=0\\5-3x=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=2\\3x=5\end{cases}}\Rightarrow\orbr{\begin{cases}x=2\\x=\frac{5}{3}\end{cases}}\)