Answer
$-1$
Work Step by Step
Step 1. Take square on both sides of the equation to get $2x+3=(x+2)^2\longrightarrow 2x+3=x^2+4x+4\longrightarrow x^2+2x+1=0\longrightarrow (x+1)^2=0$ thus $x=-1$
Step 2. Check the answer with the original equation and it fits.