Two cube states are symmetric if one is a rotation or reflection of the other. In such cases, each cube can be solved using a rotation or reflection of the solution to the other cube.
The following cubes are all equivalent due to symmetries:




Original  Colour rotation  Reflection  Cube rotation 
As a result, all 4 cases can be solved using rotations and/or reflections of the same general solution. Or in other words, it should not be necessary to solve the above problem 4 times, but rather see that really they are all the same problem.