a) \(6x^2-11x+3=0\)
\(\Leftrightarrow6x^2-2x-9x+3=0\)
\(\Leftrightarrow2x\left(3x-1\right)-3\left(3x-1\right)=0\)
\(\Leftrightarrow\left(2x-3\right)\left(3x-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}2x-3=0\\3x-1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\frac{3}{2}\\x=\frac{1}{3}\end{matrix}\right.\)
b)
\(x^3+2x^2-x-2=0\)
\(\Leftrightarrow x^2\left(x+2\right)-\left(x-2\right)=0\)
\(\Leftrightarrow\left(x^2-1\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x+2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-1=0\\x+1=0\\x+2=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=1\\x=-1\\x=-2\end{matrix}\right.\)
