Chapter 5 - Section 5.8 - Solving Equations by Factoring and Problem Solving - Exercise Set - Page 323: 41

$r=\{ -5,0,2 \}$

The factored form of the given expression, $ 2r^3+6r^2=20r $, is \begin{array}{} 2r^3+6r^2-20r=0 \\\\ 2r(r^2+3r-10)=0 \\\\ 2r(r+5)(r-2)=0 .\end{array} Equating each factor to zero, then \begin{array}{l} 2r=0 \\ r=0 ,\text{ OR}\\\\ r+5=0 \\ r=0-5 \\ r=-5 ,\text{ OR}\\\\ r-2=0 \\ r=0+2 \\ r=2 \end{array} Hence, $ r=\{ -5,0,2 \} $.