x = 0 is one of them. Factoring out x^2 leaves you with the binomial equation
9x^2 -24x +16 = 0, which can be factored to
(3x -4)^2 = 0
That tells you that the other root is x = 4/3.
Normally, a 4th order equation of this type would have four solutions, some of which may be complex. This one has two real "double roots".
9x^4-24x^3+16x^2 (Find all solutions!)
2 answers
By the way, this is not trigonometry. It is algebra.