The normal to the curve

\(y=\frac{\ln(3x^2+2)}{x+1}\)

at the point \(A\) on the curve where \(x=0\), meets the \(x\)-axis at point \(B\). Point \(C\) has coordinates \((0,3\ln2)\). Find the gradient of the line \(BC\) in terms of \(\ln2\).