(1) $2(x+1)-3=x+2$
$↔2x-1=x+2$
$↔x=3$
(2) $\dfrac{1}{2}+\dfrac{3y-1}{6}=\dfrac{10}{3}$
$↔\dfrac{3y-1}{6}=\dfrac{17}{6}$
$↔3y-1=17$
$↔3y=18$
$↔y=6$
(3) $\dfrac{6(z²-1)}{5}=z²+z$
$↔6(z²-1)=5(z²+z)$
$↔6z²-6=5z²+5z$
$↔z²-5z-6=0$
$↔(z-6)(z+1)=0$
$↔z-6=0\quad or\quad z+1=0$
$↔z=6\quad or\quad z=-1$