a)
\(x\left(2x-3\right)-6+4x=0\\ x\left(2x-3\right)-2\left(3-2x\right)=0\\ x\left(2x-3\right)+2\left(2x-3\right)=0\\ \left(2x-3\right)\left(x+2\right)=0\\ \left[{}\begin{matrix}2x-3=0\\x+2=0\end{matrix}\right.\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-2\end{matrix}\right.\)
b)
\(x^3+2x^2+x=0\\ x\left(x^2+2x+1\right)=0\\ x\left(x+1\right)^2=0\\ \left[{}\begin{matrix}x=0\\x+1=0\end{matrix}\right.\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)
c)
\(x^2-6x+8=0\\ x^2-2x-4x+8=0\\ x\left(x-2\right)-4\left(x-2\right)=0\\ \left(x-2\right)\left(x-4\right)=0\\ \left[{}\begin{matrix}x-2=0\\x-4=0\end{matrix}\right.\left[{}\begin{matrix}x=2\\x=4\end{matrix}\right.\)
a) \(x\left(2x-3\right)-6+4x=0\)
\(\Leftrightarrow x\left(2x-3\right)+2\left(2x-3\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(2x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=0\\2x-3=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=\dfrac{3}{2}\end{matrix}\right.\)
b) \(x^3+2x^2+x=0\)
\(\Leftrightarrow x\left(x^2+2x+1\right)=0\)
\(\Leftrightarrow x\left(x+1\right)^2=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)
c) \(x^2-6x+8=0\)
\(\Leftrightarrow x^2-2x-4x+8=0\)
\(\Leftrightarrow x\left(x-2\right)-4\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\x-2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=2\end{matrix}\right.\)
