\(4x^2-12x+5=0\\ \Leftrightarrow4x^2-2x-10x+5=0\\ \Leftrightarrow2x\left(2x-1\right)-5\left(2x-1\right)=0\\ \Leftrightarrow\left(2x-5\right)\left(2x-1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}2x-5=0\\2x-1=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}2x=5\\2x=1\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=\dfrac{1}{2}\end{matrix}\right.\)
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