We are given that the equation f(x)=0 has a solution at x=3. Using this information we have to find as many solutions as possible of the equations
1) 2f(x+5)=0 and 2. $\displaystyle \left | f(x) \right |=0 $
1. $\displaystyle 2f(x+5) = 0$ is equivalent to $\displaystyle f(x+5) = 0$.
Since you know $\displaystyle f(3) = 0$, set $\displaystyle f(x+5) = f(3)$.
This much gives you at least $\displaystyle x + 5 = 3; x = -2$.
2. $\displaystyle |f(x)| = 0$ has the same roots as $\displaystyle f(x) = 0$.