Factoring the polynomial $3(2x+3)^2 + 7(2x+3) - 6$ 
Factor $3(2x+3)^2 + 7(2x+3) - 6$

What I did:
With the substitution $X=2x+3$:
\begin{align}
3(2x+3)^2 + 7(2x+3) - 6
&= 3X^2-9X+2X-6 \\
&= 3X(X-3)+2(X-3) \\
&= (X-3)(3X+2) \\
&=((2x+3)-3)(3(2x+3)+2) \\
&=(2x+0)(6x+9+2) \\
&=(2x)(6x+11)
\end{align}

Your method is correct. You made a sign error:
$$...=(X+3)(3X-2)=...$$
