Question 74468
{{{(cross(2x)(5x-10))/cross(2x)=0}}}Divide both sides by 2x
{{{5x-10=0}}}
{{{5x=10}}}
{{{x=2}}}There's one answer
Go back to the original problem
{{{(2x*cross(5x-10))/cross((5x-10))=0}}}Divide both sides by (5x-10)
{{{2x=0}}}
{{{x=0}}}There's the other answer. The reason why you have 2 answers is because when x is 0 or 2 (notice the or) then the entire equation equals zero. If I plug in x=0 then I get
{{{2(0)(5(0)-10)=0}}}
{{{0(0-10)=0}}}
{{{0(-10)=0}}}
{{{0=0}}}works
{{{2(2)(5(2)-10)=0}}}
{{{4(10-10)=0}}}
{{{4(0)=0}}}
{{{0=0}}}works
So in a general sense if I have
{{{pq=0}}} then I can set either p or q equal to zero to solve for p and q since 0 times anything is 0. 
So the solution is 
{{{p=0}}} or {{{q=0}}}
So the answer is x=0 or x=2
Also, notice if you graph {{{2x(5x-10)}}} the x-intercepts will be x=0 and x=2. These are points when y=0
{{{ graph( 300, 200, -6, 5, -10, 10, 2x*(5x-10)) }}}Graph of {{{2x(5x-10)}}}