Given the equation

you should have in mind that the expression x^2-9 and x^3-8 are "numbers" and that the product of two numbers is zero if and only if one of the numbers is zero. Then, by using this, you get the following auxiliary equations

which is equivalent to
![x=\sqrt[]{9}](https://img.qammunity.org/2023/formulas/mathematics/college/tfgowpvt6oryx10sckkyj08c6zobt1yhk5.png)
so x=3 o x=-3.
Finally, for the other case

So
![x=\sqrt[3]{8}=2](https://img.qammunity.org/2023/formulas/mathematics/college/16kwubf61nabzo3g4ubbjy2ou67r88wmap.png)
so the three possible solutions for the equation are x=3, x=-3 and x=2