a ) \(5\left(x+3\right)-6x-2x^2=0\)
\(\Leftrightarrow5\left(x+3\right)-2x\left(3+x\right)=0\)
\(\Leftrightarrow\left(5-2x\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}5-2x=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=5\\x=-3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=-3\end{matrix}\right.\)
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b ) \(\left(x-2004\right)=8016x-4x^2\)
\(\Leftrightarrow x-2004=-4x\left(x-2004\right)\)
\(\Leftrightarrow x-2004+4x\left(x-2004\right)=0\)
\(\Leftrightarrow\left(x-2004\right)\left(4x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2004=0\\4x+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2004\\4x=-1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2004\\x=-\dfrac{1}{4}\end{matrix}\right.\)
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c ) \(\left(x+1\right)^2=x+1\)
\(\Leftrightarrow\left(x+1\right)^2-\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left[\left(x+1\right)-1\right]=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x+1-1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=0\end{matrix}\right.\)
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