The sum of the real roots of the equation $\left|\begin{array}{ccc}x& -6& -1\\ 2& -3x& x-3\\ -3& 2x& x+2\end{array}\right|=0$ is equal to 

$We have \left|\begin{array}{ccc}x& -6& -1\\ 2& -3x& x-3\\ -3& 2x& x+2\end{array}\right|=0$

$\Rightarrow \begin{array}{l}\Rightarrow x\left(-3x^2-6x-2x^2+6x\right)+6(2x+4+3x-9)-1(4x-9x)=0\\ x^3-7x+6=0\\ The roots are 1,2,-3.\end{array}$

$\therefore sum of roots =1+ 2-3=0$