I need help on this Homework question and also please give the steps on what lead to the answer.

The function is given by:
[tex]f(x)=x(x^2+7)(x^2-8)[/tex]The three quantities are zero then it follows:
[tex]\begin{gathered} x=0;x^2+7=0;x^2-8=0 \\ x=0;x^2=-7;x^2=8 \\ x=0,x=\pm\sqrt[]{7}i;x=\pm2\sqrt[]{2} \end{gathered}[/tex]Option D is correct.