Chapter 1 - Equations and Inequalities - Chapter 1 Test Prep - Review Exercises - Page 179: 81

$-15$, $\frac{5}{2}$

Step 1. Let $u=(2x+3)^{1/3}$, the original equation becomes $u^2+u-6=0$ Step 2. Factor the equation to get $(u+3)(u-2)=0$ which gives $u=-3$ and $u=2$ Step 3. For $u=-3$, we have $(2x+3)^{1/3}=-3$, $2x+3=-27$, thus $x=-15$ Step 4. For $u=2$, we have $(2x+3)^{1/3}=2$, $2x+3=8$, thus $x=\frac{5}{2}$