a) $x-14=3x+18$
$2x=-32$
$x=-16$
b) $2(x-5)-3(x-4)=-6+15(-3)$
$-x+2=-51 $
$x=53$
c) $(x+7)(x-9)=0$
$\left[ \begin{array}{l}x+7=0\\x-9=0\end{array} \right.$
$\left[ \begin{array}{l}x=7\\x=9\end{array} \right.$
d) $|2x-5|-7=22$
$|2x-5| =29$
$\left[ \begin{array}{l}2x-5=29\\x2x-5=-29\end{array} \right.$
$\left[ \begin{array}{l}x=17\\x=-12\end{array} \right.$