Question

$$3u^{6}-3u^{4}+64=0$$

Solve for u

$u\in -\frac{i\sqrt{3\left(-\sqrt[3]{24\sqrt{143}-287}-\sqrt[3]{-24\sqrt{143}-287}-1\right)}}{3},\frac{i\sqrt{3\left(-\sqrt[3]{24\sqrt{143}-287}-\sqrt[3]{-24\sqrt{143}-287}-1\right)}}{3},\frac{e^{\frac{3\arctan(\frac{\sqrt{3}\left(\sqrt[3]{24\sqrt{143}-287}-1\right)}{\sqrt[3]{24\sqrt{143}-287}-2\sqrt[3]{-24\sqrt{143}-287}+1})i+7\pi i}{6}}\sqrt{6|-\sqrt{3}i+\sqrt[3]{24\sqrt{143}-287}-2\sqrt[3]{-24\sqrt{143}-287}+1+\sqrt{3}\sqrt[3]{24\sqrt{143}-287}i|}}{6},\frac{e^{\frac{3\arctan(\frac{\sqrt{3}\left(\sqrt[3]{24\sqrt{143}-287}-1\right)}{\sqrt[3]{24\sqrt{143}-287}-2\sqrt[3]{-24\sqrt{143}-287}+1})i+13\pi i}{6}}\sqrt{6|-\sqrt{3}i+\sqrt[3]{24\sqrt{143}-287}-2\sqrt[3]{-24\sqrt{143}-287}+1+\sqrt{3}\sqrt[3]{24\sqrt{143}-287}i|}}{6},\frac{e^{\frac{3\arctan(\frac{\sqrt{3}\left(-\sqrt[3]{24\sqrt{143}-287}+1\right)}{\sqrt[3]{24\sqrt{143}-287}-2\sqrt[3]{-24\sqrt{143}-287}+1})i+5\pi i}{6}}\sqrt{6|-\sqrt{3}\sqrt[3]{24\sqrt{143}-287}i+\sqrt[3]{24\sqrt{143}-287}-2\sqrt[3]{-24\sqrt{143}-287}+1+\sqrt{3}i|}}{6},\frac{e^{\frac{3\arctan(\frac{\sqrt{3}\left(-\sqrt[3]{24\sqrt{143}-287}+1\right)}{\sqrt[3]{24\sqrt{143}-287}-2\sqrt[3]{-24\sqrt{143}-287}+1})i+11\pi i}{6}}\sqrt{6|-\sqrt{3}\sqrt[3]{24\sqrt{143}-287}i+\sqrt[3]{24\sqrt{143}-287}-2\sqrt[3]{-24\sqrt{143}-287}+1+\sqrt{3}i|}}{6}$