$$(6x^8-120x^6+900x^4-3000x^2+3750)^2 = 0$$
Answer
$$ \begin{matrix}x_1 = 1.21097 & x_2 = -1.21097 & x_3 = 3.85046 \\[1 em] x_4 = -3.85046 & x_5 = 0.51232+0.98527i & x_6 = 0.51232-0.98527i \\[1 em] x_7 = -0.51232+0.98527i & x_8 = -0.51232-0.98527i & x_9 = 2.2746+1.77013i \\[1 em] x_10 = 2.2746-1.77013i & x_11 = -2.2746+1.77013i & x_12 = -2.2746-1.77013i \\[1 em] x_13 = 3.43551+1.13188i & x_14 = 3.43551-1.13188i & x_15 = -3.43551+1.13188i \\[1 em] x_16 = -3.43551-1.13188i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (6x^8-120x^6+900x^4-3000x^2+3750)^2 &= 0&& \text{simplify left side} \\[1 em]36x^{16}-1440x^{14}+25200x^{12}-252000x^{10}+1575000x^8-6300000x^6+15750000x^4-22500000x^2+14062500 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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