Symmetric "easy looking" polynomial problem

Hi Folks,

here's a problem I have been trying to solve for the last few months for my research.

Every time I get to a point which almost looks like solvable but I am unable to crack it. Please give a try or offer your suggestions.

All I want to solve is the solution of 'd' in:

(1/Q^2 + (2 d + g)^2) (1/Q^2 + (2 d - g)^2) (1/

Q^2 + (2 d + 2 g)^2) (1/Q^2 + (2 d - 2 g)^2) =

2 (1 + g^2 Q^2) (1 + 4 g^2 Q^2) (1 + 9 g^2 Q^2)

where, g and Q are constants and 'd' is what I am interested to solve.

Solving numerically, I set of positive and negative solutions of equal magnitude of 'd' but I am not able to exploit this condition to solve for 'd'