12x2+11x-15=0
12y-8y-15=0
s2+10s=0
5w2=20w
When we factor we get
$\displaystyle 12x^2-11x-15=(4x+3)(3x-5)$
$\displaystyle 12y^2-8y-15=(6y+5)(2y-3)$
$\displaystyle s^2+10s=s(s+10)$
$\displaystyle 5w^2-20w=5w(w-4)$
I think I read those right from your post, on the second one I didn't know if the 12y was supposed to be squared or not. If it wasn't then just factor a y out of the first two terms and do the subtraction and simplify.
After you have them factored out you can set each factor equal to zero and solve for the possible roots.
Hope this helps.