Answer
$\{-\frac{5}{2},-2,0, \frac{1}{2}\}$
Work Step by Step
Step 1. Let $u=(x+1)^{2}$, we have $4u^2-13u+9=0$
Step 2. Factor and solve: $(u-1)(4u-9)=0$ thus $u=1,\frac{9}{4}$
Step 3. For $u=1$, we have $(x+1)^{2}=1$ or $x+1=\pm1$ thus $x=-2, 0$
Step 4. For $u=\frac{9}{4}$, we have $(x+1)^{2}=\frac{9}{4}$ or $x+1=\pm\frac{3}{2}$ thus $x=-\frac{5}{2},\frac{1}{2} $
Step 5. Solution set $\{-\frac{5}{2},-2,0, \frac{1}{2}\}$
