Chapter 2 - Linear and Quadratic Functions - Section 2.8 Equations and Inequalities Involving the Absolute Value Function - 2.8 Assess Your Understanding - Page 182: 38

$-4,-3,0,1$.

Step 1. The original equation can be separated into two cases: $x^2+3x-2=2$ or $x^2+3x-2=-2$. Step 2. For $x^2+3x-2=-2$, we have$x^2+3x=0 \longrightarrow (x)(x+3)=0 \longrightarrow x=-3,0$. Step 3. For $x^2+3x-2=2$, we have $x^2+3x-4=0 \longrightarrow (x+4)(x-1)=0 \longrightarrow x=-4,1$.