This is an almost impossible problem to solve symbolically. Why? symbolic computations using determinants become INCREDIBLY complicated. Then hoping to solve for a symbolic solution will take an immense amount of time. But even if you wait forever, that still won't happen. Why not?
I looked at your result, jacob. A quick scan through it, and I never saw the unknown theta_6. So then, I had MATLAB look for me.
F = matlabFunction(jacob)
function_handle with value:
Essentially, you have 6 equations, but NONE of them are a function of theta_6. Yes, you used it in the computations, but it got killed off somehow. I've not looked at the coefficients used or how Robot_transform uses them, but theta_6 never comes out the back end.
So in the end, you are asking solve to solve a problem with 6 equations, in 5 unknowns.
And that alone pretty much insures that solve will never find a solution. You might instead look at other approaches. For example, we can do this:
Surprisingly, that ran quite quickly. Now, we can compute the determinant of jacob as the product of the diagonal elements of the matrix U, as computed by the LU decomposition. If any of those diagonal elements is zero, then the matrix jacob will be singular. So you might decide to try a solution based on that, perhaps using a numerical optimization tool.
But hoping to solve this using symbolic tools is still impossible, at least not for some years to come.