Solve this equation

$x²-3x-10=0$

I could see that x=5 is a root for this equation (if we replace x by 5 we get 0) 

That means I can factorize this equation like that: 

$x²-3x-10 = (x-5)(x+2)$

$\Rightarrow (x-5)(x+2)=0$

$x-5=0 \Rightarrow x=5$or

$x+2=0 \Rightarrow x=-2$