\(3x^4+2x^3-10x^2+2x+3=0\)
\(\Leftrightarrow3x^4-6x^3+3x^2+8x^3-16x^2+8x+3x^2-6x+3=0\)
\(\Leftrightarrow3x^2\left(x^2-2x+1\right)+8x\left(x^2-2x+1\right)+3\left(x^2-2x+1\right)=0\)
\(\Leftrightarrow\left(x^2-2x+1\right)\left(3x^2+8x+3\right)=0\)
\(\Leftrightarrow\left(x-1\right)^2\left(3x^2+8x+3\right)=0\)
\(\Leftrightarrow\left(x-1\right)^2\left(3\left(x+\dfrac{4}{3}\right)^2-\dfrac{7}{3}\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-1=0\\3\left(x+\dfrac{4}{3}\right)^2-\dfrac{7}{3}=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{-8\pm\sqrt{28}}{6}\end{matrix}\right.\)
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