2) \(y\left(y-\dfrac{1}{2}\right)\left(2y+5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}y=0\\y-\dfrac{1}{2}=0\\2y+5=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}y=0\\y=\dfrac{1}{2}\\2y=-5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}y=0\\y=\dfrac{1}{2}\\y=-\dfrac{5}{2}\end{matrix}\right.\)
6) \(\left(y^2-2y+1\right)-9=0\)
\(\Leftrightarrow\left(y-1\right)^2-3^2=0\)
\(\Leftrightarrow\left(y-1-3\right)\left(y-1+3\right)=0\)
\(\Leftrightarrow\left(y-4\right)\left(y+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}y=4\\y=-2\end{matrix}\right.\)
8) \(\left(x-3\right)^2-\left(x+1\right)^2=0\)
\(\Leftrightarrow\left(x-3+x+1\right)\left(x-3-x-1\right)=0\)
\(\Leftrightarrow-4\left(2x-2\right)=0\)
\(\Leftrightarrow2x=2\)
\(\Leftrightarrow x=\dfrac{2}{2}\)
\(\Leftrightarrow x=1\)
10) \(\left(3x-7\right)^2-4\left(x+1\right)^2=0\)
\(\Leftrightarrow\left(3x-7-2x-2\right)\left(3x-7+2x+2\right)=0\)
\(\Leftrightarrow\left(x-9\right)\left(5x-5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-9=0\\5x-5=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=9\\5x=5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=9\\x=1\end{matrix}\right.\)
12) \(2x\left(x-5\right)-x\left(3+2x\right)=26\)
\(\Leftrightarrow2x^2-10x-3x-2x^2=26\)
\(\Leftrightarrow-13x=26\)
\(\Leftrightarrow x=\dfrac{26}{-13}\)
\(\Leftrightarrow x=-2\)
