a) \(5\left(3y+1\right)\left(4y-3\right)>0\Leftrightarrow\left(3y+1\right)\left(4y-3\right)>0\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}3y+1>0\\4y-3>0\end{matrix}\right.\\\left[{}\begin{matrix}3y+1< 0\\4y-3< 0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}3y>-1\\4y>3\end{matrix}\right.\\\left[{}\begin{matrix}3y< -1\\4y< 3\end{matrix}\right.\end{matrix}\right.\) \(\left\{{}\begin{matrix}\left[{}\begin{matrix}y>\dfrac{-1}{3}\\y>\dfrac{3}{4}\end{matrix}\right.\\\left[{}\begin{matrix}y< \dfrac{-1}{3}\\y< \dfrac{3}{4}\end{matrix}\right.\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}y>\dfrac{3}{4}\\y< -\dfrac{1}{3}\end{matrix}\right.\) vậy \(y>\dfrac{3}{4}\) hoặc \(y< \dfrac{-1}{3}\)

b) \(2y^2-4y\le0\Leftrightarrow2y\left(y-2\right)\le0\Leftrightarrow y\left(y-2\right)\le0\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}y\ge0\\y-2\le0\end{matrix}\right.\\\left[{}\begin{matrix}y\le0\\y-2\ge0\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}y\ge0\\y\le2\end{matrix}\right.\\\left[{}\begin{matrix}y\le0\\y\ge2\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}0\le y\le2\\y\in\varnothing\end{matrix}\right.\) vậy \(0\le y\le2\)