Chapter 5 - Section 5.8 - Solving Equations by Factoring and Problem Solving - Exercise Set - Page 323: 55

$x=\left\{ -5,0,5 \right\}$

The factored form of the given expression, $ 2x^3=50x $, is \begin{array}{l} 2x^3-50x=0 \\\\ 2x(x^2-25)=0 \\\\ 2x(x+5)(x-5)=0 .\end{array} Equating each factor to zero, then \begin{array}{l} 2x=0 \\ x=\dfrac{0}{2} \\ x=0 ,\text{ OR}\\\\ x+5=0 \\ x=0-5 \\ x=-5 ,\text{ OR}\\\\ x-5=0 \\ x=0+5 \\ x=5 \end{array} Hence, $ x=\left\{ -5,0,5 \right\} $.