Solve y=(1/6-t^2)^2

$$y = ( \frac { 1 } { 6 - t ^ { 2 } } ) ^ { 2 }$$

Solve for t (complex solution)

$$t=\sqrt{y^{-\frac{1}{2}}+6}$$

$$t=-\sqrt{y^{-\frac{1}{2}}+6}$$

$$t=-\sqrt{6-y^{-\frac{1}{2}}}$$

$$t=\sqrt{6-y^{-\frac{1}{2}}}\text{, }y\neq 0$$

Solve for y (complex solution)

$$y=\frac{1}{\left(t^{2}-6\right)^{2}}$$

$$t\neq -\sqrt{6}\text{ and }t\neq \sqrt{6}$$

Solve for t

$$\left\{\begin{matrix}t=-\frac{\sqrt{6\sqrt{y}+1}}{\sqrt[4]{y}}\text{; }t=\frac{\sqrt{6\sqrt{y}+1}}{\sqrt[4]{y}}\text{, }&y>0\\t=-\frac{\sqrt{6\sqrt{y}-1}}{\sqrt[4]{y}}\text{; }t=\frac{\sqrt{6\sqrt{y}-1}}{\sqrt[4]{y}}\text{, }&y\geq \frac{1}{36}\end{matrix}\right.$$

Solve for y

$$y=\frac{1}{\left(t^{2}-6\right)^{2}}$$

$$|t|\neq \sqrt{6}$$