Solving unknwon matrix in a matrix equation using symbolic and kronecker

Hi, I need some help on how to solve the matrix equation below in MATLAB. I tried doing it using the symbolic toolbox and kronecker function but I am not able to obtain the final P matrix shown below. I wonder if MATHCAD is my best option to solve it. Any help is appreciated.

Here are the different matrices. L is a matrix as well. wp, wc and wv are constants.

Here is the resulting P matrix I need to get.

[Torsten]

Why do you need to solve if you know the solution ?

[mpz]

@Torsten I am trying to know how to derive this one because I have a similar problem and I would like to know how this one was derived. Trying to not have to do it analytically.