\(x^4+4x^3-5x^2-38x-30=0\)
\(\Leftrightarrow x^4-2x^3-3x^2+6x^3-12x^2-18x+10x^2-20x-30=0\)
\(\Leftrightarrow x^2\left(x^2-2x-3\right)+6x\left(x^2-2x-3\right)+10\left(x^2-2x-3\right)=0\)
\(\Leftrightarrow\left(x^2-2x-3\right)\left(x^2+6x+10\right)=0\)
\(\Leftrightarrow\left(x^2-3x+x-3\right)\left(x^2+6x+10\right)=0\)
\(\Leftrightarrow\left[x\left(x-3\right)+\left(x-3\right)\right]\left(x^2+6x+10\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-3\right)\left(x^2+6x+10\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x+1=0\\x-3=0\\x^2+6x+10=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=-1\\x=3\\x^2+6x+9+1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-1\\x=3\\\left(x+3\right)^2+1>0\left(loai\right)\end{matrix}\right.\)