[tex](x+2)(3x+1)=0\\\\\text{The product is equal to 0 if one of the factors is equal to 0.}\\\\x+2=0\ \vee\ 3x+1=0\\\\x+2=0\qquad\text{subtract 2 from both sides}\\\boxed{x=-2}\\\\3x+1=0\qquad\text{subtract 1 from both sides}\\3x=-1\qquad\text{divide both sides by 3}\\\boxed{x=-\dfrac{1}{3}}[/tex]
