Solve d=0-y*sy*s

$$d = 0 - y \cdot s y \cdot s$$

Solve for d

$$d=-\left(sy\right)^{2}$$

Solution Steps

Multiply y and y to get y^{2}.

$$d=0-y^{2}ss$$

Multiply s and s to get s^{2}.

$$d=0-y^{2}s^{2}$$

Reorder the terms.

$$d=-s^{2}y^{2}$$

Solve for s (complex solution)

$$\left\{\begin{matrix}s=-\frac{i\sqrt{d}}{y}\text{; }s=\frac{i\sqrt{d}}{y}\text{, }&y\neq 0\\s\in \mathrm{C}\text{, }&d=0\text{ and }y=0\end{matrix}\right.$$

Solve for s

$$\left\{\begin{matrix}s=\frac{\sqrt{-d}}{y}\text{; }s=-\frac{\sqrt{-d}}{y}\text{, }&d\leq 0\text{ and }y\neq 0\\s\in \mathrm{R}\text{, }&d=0\text{ and }y=0\end{matrix}\right.$$