A. 2x (3x-2) - (3x-2)=0
➜\(\left(2x-1\right)\left(3x-2\right)=0\)
➜\(\left[{}\begin{matrix}2x-1=0\\3x-2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{1}{2}\\x=\frac{2}{3}\end{matrix}\right.\)
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B. (x+1) (3-x) +x=0
➜\(3x-x^2+3-x+x=0\)
➜\(3x-x^2=0\)
➜\(x\left(3-x\right)=0\Rightarrow\left[{}\begin{matrix}x=0\\3-x=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)
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C. (x-2)^2 = (2x+3)^2
➞\(\left(x-2\right)^2-\left(2x+3\right)^2=0\)
➜\(\left(x-2-2x-3\right)\left(x-2+2x+3\right)=0\)
➜\(\left[{}\begin{matrix}x-2-2x-3=0\\x-2+2x+3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-5\\x=\frac{-1}{3}\end{matrix}\right.\)
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D. x^2 -5x+6=0
➜\(x^2-2x-3x+6=0\)
➜\(x\left(x-2\right)-3\left(x-2\right)=0\)
➜\(\left(x-3\right)\left(x-2\right)=0\)
➜\(\left[{}\begin{matrix}x-2=0\\x-3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=3\end{matrix}\right.\)
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