\(4x^3-16x^2+19x-6=0\)
\(\Leftrightarrow4x^3-8x^2-8x^2+16x+3x-6=0\)
\(\Leftrightarrow\left(x-2\right)\left(4x^2-8x+3\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(2x-3\right)\left(2x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{3}{2}\\x=\dfrac{1}{2}\end{matrix}\right.\)