a) \(x\left(2x+7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\2x+7=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\2x=-7\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{7}{2}\end{matrix}\right.\)
b) \(x\left(2x+7\right)>0\)
\(TH1:\left\{{}\begin{matrix}x>0\\2x+7>0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x>0\\x>-\dfrac{7}{2}\end{matrix}\right.\) \(\Leftrightarrow x>0\)
\(TH2:\left\{{}\begin{matrix}x< 0\\2x+7< 0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x< 0\\x< -\dfrac{7}{2}\end{matrix}\right.\) \(\Leftrightarrow x< -\dfrac{7}{2}\)
Vậy \(x>0\) hay \(x< -\dfrac{7}{2}\)
c) \(x\left(2x+7\right)< 0\)
\(TH1:\left\{{}\begin{matrix}x>0\\2x+7< 0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x>0\\x< -\dfrac{7}{2}\end{matrix}\right.\) (Vô lý nên loại)
\(TH2:\left\{{}\begin{matrix}x< 0\\2x+7>0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x< 0\\x>-\dfrac{7}{2}\end{matrix}\right.\) \(\Leftrightarrow-\dfrac{7}{2}< x< 0\)
Vậy \(-\dfrac{7}{2}< x< 0\)