  We develop a systematic way to solve linear equations involving tensors of
arbitrary rank. We start off with the case of a rank $3$ tensor, which appears
in many applications, and after finding the condition for a unique solution we
derive this solution. Subsequently we generalize our result to tensors of
arbitrary rank. Finally we consider a generalized version of the former case of
rank $3$ tensors and extend the result when the tensor traces are also
included.
