Chapter 1 - Equations and Inequalities - Chapter 1 Test Prep - Review Exercises - Page 179: 82

$-4, -2\frac{26}{27}$

Step 1. Let $u=(x+3)^{-1/3}$, the original equation becomes $u^2-2u-3=0$ which gives $u=-1$ and $u=3$ Step 2. For $(x+3)^{-1/3}=-1$, we have $(x+3)^{1/3}=-1\longrightarrow x+3=(-1)^3$, thus $x=-4$ Step 3. For $(x+3)^{-1/3}=3$, we have $(x+3)^{1/3}=\frac{1}{3}\longrightarrow x+3=(\frac{1}{3})^3$, thus $x=-3+\frac{1}{27}=-2\frac{26}{27}$