You have to be more specific in your inquiries that simply stating "help me understand".  Click on a particular solution step and review the logic which is employed.  The next two inquiries are single variables and that single variable is being solved for... it's hard to guess what specific portion you want to ask about. 

In both of those, you are solving an equation which has been set equal to zero, so any product in the left side can be solved for "0" [zero].  If x(x+3)=0 then if x=0 that is a solution and if x=-3, then -3+3=0, so the solution set in such an example would be {-3,0}.  Your equations solve for 'w' and then for 's' with the same logic... "what factor will reduce an expression to zero" and the answer is "zero multiplied times _anything_ equals zero".