a) \(\left(3x+2\right)\left(x^2+1\right)=\left(9x^2-4\right)\left(x+1\right)\)
\(\Leftrightarrow\left(3x+2\right)\left(x^2+1\right)-\left(3x+2\right)\left(3x-2\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left(3x+2\right)\left[x^2+1-\left(3x^2+3x-2x-2\right)\right]=0\)
\(\Leftrightarrow\left(3x+2\right)\left(-2x^2-x+3\right)=0\)
\(\Leftrightarrow\left(3x+2\right)\left(-2x^2+2x-3x+3\right)=0\)
\(\Leftrightarrow\left(3x+2\right)\left[-2x\left(x-1\right)-3\left(x-1\right)\right]=0\)
\(\Leftrightarrow\left(3x+2\right)\left(-2x-3\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x+2=0\\-2x-3=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-2}{3}\\x=-1,5\\x=1\end{matrix}\right.\)
b) \(x\left(2x-9\right)=3x\left(x-5\right)\)
\(\Leftrightarrow2x^2-9x-3x^2+15x=0\)
\(\Leftrightarrow-x^2+6x=0\)
\(\Leftrightarrow-x\left(x+6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+6=0\Leftrightarrow x=-6\end{matrix}\right.\)
