TeX source:
\begin{array}{rclcll}\mathbb{D} &=& \mathbb{R} \\\\-\dfrac{1}{81}z^3\left(9z\left(-9z^4+2\right)\right) &=& \dfrac{2}{27} \\\\-\dfrac{1}{81}z^3\left(-81z^5+18z\right) &=& \dfrac{2}{27} \\\\z^8-\dfrac{2}{9}z^4 &=& \dfrac{2}{27} &\vert & -\dfrac{2}{27} \\\\z^8-\dfrac{2}{9}z^4-\dfrac{2}{27} &=& 0 \\\end{array}