If the line (x-y+1)+k(y-2x+4)=0 makes equal intercepts on the axes then the value of 3k is _________

Given line (x-y+1)+k(y-2x+4)=0

$$\begin{gathered} \Rightarrow x(1-2k)+y(k-1)=-(4k+1) \\ \Rightarrow \frac{x}{{\displaystyle \frac{-(4k+1)}{1-2k}}}+\frac{y}{\frac{-(4k+1)}{k-1}}=1 \\ Since line makes equal intercepts then \\ \frac{-(4k+1)}{1-2k}=\frac{-(4k+1)}{k-1} \\ \Rightarrow k-1=1-2k \\ \Rightarrow k=\frac{2}{3} \end{gathered}$$