First of all, move all terms to the same side:
[tex] x^3 + 3x^2 - 8 x = 0 [/tex]
You can factor an x, which means that [tex] x = 0[/tex] is a solution:
[tex] x(x^2+3x-8) [/tex]
This expression is further factorizable if the quadratic equation has any solution. Using the quadratic formula, we can find that they are
[tex] x_{1,2} = -\dfrac{3 \pm \sqrt{41}}{2}[/tex]
So, we have
[tex] x(x^2+3x+8) = 0 = \iff x = 0,\quad x =-\dfrac{3 + \sqrt{41}}{2} ,\quad x =-\dfrac{3 - \sqrt{41}}{2}[/tex]
