If the equations $K(6x^2+3)+rx+2x^2-1=0$ and $6K(2x^2+1)+px+4x^2-2=0$ have both the roots common, then the value of $2r-p$ is

$\begin{array}{l}K(6x^2+3)+rx+2x^2-1=0\\ x^2(6K+2)+rx+3K-1=0\to \left(1\right)\\ 6K(2x^2+1)+px+4x^2-2=0\\ x^2(12K+4)+px+6K-2=0\to \left(2\right)\end{array}$

Equations (1) and (2) have both roots are common, then

$\begin{array}{l}\frac{6K+2}{12K+4}=\frac{r}{p}=\frac{3K-1}{2(3K-1)}\\ \frac{r}{p}=\frac{1}{2}\\ 2r=p\\ 2r-p=0\end{array}$