[tex]8f^2+14f+5=0\\\\8f^2+10f+4f+5=0\\\\2f(4f+5)+1(4f+5)=0\\\\(4f+5)(2f+1)=0\iff4f+5=0\ \vee\ 2f+1=0\\\\4f+5=0\qquad\text{subtract 5 from both sides}\\\\4f=-5\qquad\text{divide both sides by 4}\\\\f=-\dfrac{5}{4}\\\\2f+1=0\qquad\text{subtract 1 from both sides}\\\\2f=-1\qquad\text{divide both sides by 2}\\\\f=-\dfrac{1}{2}\\\\Answer:\ \boxed{f=-\dfrac{5}{4}\ \vee\ f=-\dfrac{1}{2}}[/tex]
