The zeros of a function f are found by solving the equation f(x) = 0. Then, you have
[tex]\begin{gathered} f(x)=x(x+5)(x-7) \\ 0=x(x+5)(x-7) \end{gathered}[/tex]
Then as a product of factors, it is zero if and only if one or more of the factors is zero, you have
[tex]x=0[/tex][tex]\begin{gathered} x+5=0 \\ x+5-5=0-5 \\ x=-5 \end{gathered}[/tex][tex]\begin{gathered} x-7=0 \\ x-7+7=0+7 \\ x=7 \end{gathered}[/tex]
Therefore, the zeros of this function will be
[tex]x=0,\text{ }x=-5\text{ and }x=7[/tex]
