a, \(\Leftrightarrow3x\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x=0\\x-2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)
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b, \(\Leftrightarrow\left(x-6\right)\left(x+10\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-6=0\\x+10=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=6\\x=-10\end{matrix}\right.\)
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c, \(\Leftrightarrow\left(x+2\right)^2-\left(x+2\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x+2-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=0\\x+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=-1\end{matrix}\right.\)
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\(a.\)
\(3x^2-6x=0\)
\(\Leftrightarrow3x\cdot\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x=0\\x-2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)
\(b.\)
\(x\cdot\left(x-6\right)+10\cdot\left(x-6\right)=0\)
\(\Leftrightarrow\left(x-6\right)\cdot\left(x+10\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-6=0\\x+10=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=6\\x=-10\end{matrix}\right.\)
\(c.\)
\(\left(x+2\right)^2=x+2\)
\(\Leftrightarrow x^2+4x+4-x-2=0\)
\(\Leftrightarrow x^2+3x+2=0\)
\(\Leftrightarrow\left(x+1\right)\cdot\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x+2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-2\end{matrix}\right.\)
