\(x^4-25x^2+60x-36=0\)
\(\Leftrightarrow x^4+5x^3-6x^2-5x^3-25x^2+30x+6x^2+30x-36=0\)
\(\Leftrightarrow x^2\left(x^2+5x-6\right)-5x\left(x^2+5x-6\right)+6\left(x^2+5x-6\right)=0\)
\(\Leftrightarrow\left(x^2-5x+6\right)\left(x^2+5x-6\right)=0\)
\(\Leftrightarrow\left(x^2-2x-3x+6\right)\left(x^2-x+6x-6\right)=0\)
\(\Leftrightarrow\left[x\left(x-2\right)-3\left(x-2\right)\right]\left[x\left(x-1\right)+6\left(x-1\right)\right]=0\)
\(\Leftrightarrow\left(x-3\right)\left(x-2\right)\left(x-1\right)\left(x+6\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-3=0\\x-2=0\\x-1=0\\x+6=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=3\\x=2\\x=1\\x=-6\end{matrix}\right.\)
