1, $x^2-2x-3=0$
$⇔x^2-3x+x-3=0$
$⇔x(x-3)+(x-3)=0$
$⇔(x-3)(x+1)=0$
$⇔$\(\left[ \begin{array}{l}x-3=0\\x+1=0\end{array} \right.\)
$⇔$\(\left[ \begin{array}{l}x=3\\x=-1\end{array} \right.\)
2, $8x^2-10x+3=0$
$⇔(x-3/4)(x-1/2)=0$
$⇔$\(\left[ \begin{array}{l}x-3/4=0\\x-1/2=0\end{array} \right.\)
$⇔$\(\left[ \begin{array}{l}x=3/4\\x=1/2\end{array} \right.\)
3, $x^2-4x-21=0$
$⇔x^2-7x+3x-21=0$
$⇔x(x-7)+3(x-7)=0$
$⇔(x-7)(x+3)=0$
$⇔$\(\left[ \begin{array}{l}x-7=0\\x+3=0\end{array} \right.\)
$⇔$\(\left[ \begin{array}{l}x=7\\x=-3\end{array} \right.\)
4, $16x^2-40x+21=0$
$⇔(x-7/4)(x-3/4)=0$
$⇔$\(\left[ \begin{array}{l}x-7/4=0\\x-3/4=0\end{array} \right.\)
$⇔$\(\left[ \begin{array}{l}x=7/4\\x=3/4\end{array} \right.\)
5, $x^2-24+144=0$
$⇔(x-12)^2=0$
$⇔x-12=0$
$⇔x=12$
