\(\left(3b^2+2b+1\right)-\left(b^2+2b+3\right)=b^2+5b+4\)

\(\Leftrightarrow b^2-5b-6=0\Leftrightarrow b^2+b-6b-6=0\)

\(\Leftrightarrow b\left(b+1\right)-6\left(b+1\right)=0\Leftrightarrow\left(b-6\right)\left(b+1\right)=0\Rightarrow b=6\)