\(\left(x+1\right)\left(x+4\right)=\left(2-x\right)\left(x+2\right)\)
\(\Rightarrow x.\left(x+4\right)+\left(x+4\right)=x\left(2-x\right)+2\left(2-x\right)\)
\(\Rightarrow x^2+4x+x+4=2x-x^2+4-2x\)
\(\Rightarrow x^2+5x+4+x^2-4=0\)
\(\Rightarrow x^2+5x+x^2=0\)
\(\Rightarrow x\left(x+5+x\right)=0\)
\(\Rightarrow\left\{{}\begin{matrix}x=0\\x+5+x=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=0\\x=\frac{-5}{2}\end{matrix}\right.\)