Solve the given polynomial equation.
Use the Rational Zero Theorem, Descartes's Rule of Signs, and possibly the graph of the polynomial function shown by a graphing utility as an aid in obtaining the first root.
10x^5+59x^4+54x^3-186x^2-252x+27=0
The solution set is ?
(Use a comma to separate answers as needed. Type an exact answer, using radicals and i as needed. Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)