Hmm...This is a 4th order equation, and we only know how to solve 2nd order (quadratic) equations.
Maybe if we turned it into a quadratic by letting t = x^2 an replacing x^2 and x^4 in the original equation with t and t^2, repectively.
3x^4 -5x^2 - 2 = 0 becomes:
3t^2 -5t - 2 = 0 <--- that's a nice quadratic that we can solve using either completing the square or the quadratic formula:
(t -2)(t + 1/3) = 0 : Now substitute back for t = x^2 to get:
(x^2 - 2)(x^2 + 1/3) = 0 : now you can factor each of THOSE quadratics to get all 4 of the original factors of the original problem.
