The product is equal to 0 if one of the factors is equal to 0.
[tex](2x-1)(x+5)=0\iff2x-1=0\ \vee\ x+5=0\\\\2x-1=0\ \ \ |+1\\2x=1\ \ \ |:2\\\boxed{x=0.5}\\\\x+5=0\ \ \ \ |-5\\\boxed{x=-5}[/tex]
Answer: x = 0.5 or x = -5
