a )

$x\left(2x-7\right)-4x+14=0$

$\Rightarrow x\left(2x-7\right)-2\left(2x-7\right)=0$

$\Rightarrow\left(x-2\right)\left(2x-7\right)=0$

$\Rightarrow\left[{}\begin{matrix}x-2=0\\2x-7=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\2x=7\end{matrix}\right.$

$\Rightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{7}{2}\end{matrix}\right.$

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b )

$\left(2x+5\right)\left(3x-1\right)-\left(2x+5\right)=0$

$\Rightarrow\left(2x+5\right)\left(3x-1-1\right)=0$

$\Rightarrow\left(2x+5\right)\left(3x-2\right)=0$

$\Rightarrow\left[{}\begin{matrix}2x+5=0\\3x-2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=-5\\3x=2\end{matrix}\right.$

$\Rightarrow\left[{}\begin{matrix}x=-\dfrac{5}{2}\\x=\dfrac{2}{3}\end{matrix}\right.$

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c )

$\left(2x-3\right)^2-6x+9=0$

$\Rightarrow\left(2x-3\right)^2-3\left(2x-3\right)=0$

$\Rightarrow\left(2x-3\right)\left(2x-3-3\right)=0$

$\Rightarrow\left(2x-3\right)\left(2x-6\right)=0$

$\Rightarrow\left[{}\begin{matrix}2x-3=0\\2x-6=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=3\\2x=6\end{matrix}\right.$

$\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=3\end{matrix}\right.$

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