$$ \begin{aligned} 9x^4(3x^2-1)^2+12x^3(3x^2-1)^2+4x^2(3x^2-1)^2 &= 0&& \text{simplify left side} \\[1 em]9x^4(9x^4-6x^2+1)+12x^3(9x^4-6x^2+1)+4x^2(9x^4-6x^2+1) &= 0&& \\[1 em]81x^8-54x^6+9x^4+108x^7-72x^5+12x^3+36x^6-24x^4+4x^2 &= 0&& \\[1 em]81x^8+108x^7-54x^6-72x^5+9x^4+12x^3+36x^6-24x^4+4x^2 &= 0&& \\[1 em]81x^8+108x^7-18x^6-72x^5-15x^4+12x^3+4x^2 &= 0&& \\[1 em] \end{aligned} $$

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