\(a.2x^2+5x+3=0\\ \Leftrightarrow2x^2+2x+3x+3=0\\ \Leftrightarrow\left(2x^2+2x\right)+\left(3x+3\right)=0\\ \Leftrightarrow2x\left(x+1\right)+3\left(x+1\right)=0\\ \Leftrightarrow\left(x+1\right)\left(2x+3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x+1=0\\2x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-\frac{3}{2}\end{matrix}\right.\)
\(b.x^3+x^2+x+1=0\\\Leftrightarrow \left(x^3+x^2\right)+\left(x+1\right)=0\\ \Leftrightarrow x^2\left(x+1\right)+\left(x+1\right)=0\\\Leftrightarrow \left(x+1\right)\left(x^2+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x+1=0\\x^2+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=\varnothing\end{matrix}\right.\)