This quartic polynomial can be factored by inspection as the following:

(x^2-9)*(x^2-2) = 0

The solutions to this quartic can be calculated as the solutions to the two quadratics:

x^2 - 9 = 0 --> x^2 = 9 --> x = 3 or x = -3

OR

x^2 - 2 = 0 --> x^2 = 2 --> x = sqrt(2) ~ 1.414 or x = -sqrt(2) ~ -1.414

This gives us four total solutions. By the Fundamental Theorem of Algebra, an nth degree polynomial can have at most n distinct roots, so we must have found all roots already.

Therefore, the solutions are x = 3, -3, 1.414, -1.414

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