The original equation was $\displaystyle 4x^2+ 5x+ 1= 0$ and you used the quadratic formula to find x= -1 and x= -1/4 as solutions so that the factors are $\displaystyle (x+1)(x+ 1/4)$.
Now there are two ways to go:
1) You can multiply those factors to get $\displaystyle x^2+ x+ (1/4)x+ 1/4= x^2+ (5/4)x+ 1/4= 0$. You can then multiply both sides of that equation by 4 to get $\displaystyle 4x^2+ 5x+ 1= 0$.
2) As Shakarri said, you can immediately multiply both sides of $\displaystyle (x+ 1)(x+ 1/4)= 0$ by 4 to get $\displaystyle (x+ 1)(4x+ 1)= 0$. Then multiply that to get $\displaystyle 4x^2+ 4x+ x+ 1= 4x^2+ 5x+ 1= 0$.