Solve 5ds=d(1-s^2)

$$5 d s = d ( 1 - s ^ { 2 } )$$

Solve for d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&s=\frac{\sqrt{29}-5}{2}\text{ or }s=\frac{-\sqrt{29}-5}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply d by 1-s^{2}.

$$5ds=d-ds^{2}$$

Subtract d from both sides.

$$5ds-d=-ds^{2}$$

Add ds^{2} to both sides.

$$5ds-d+ds^{2}=0$$

Combine all terms containing d.

$$\left(5s-1+s^{2}\right)d=0$$

The equation is in standard form.

$$\left(s^{2}+5s-1\right)d=0$$

Divide 0 by 5s+s^{2}-1.

$$d=0$$

Solve for s

$$\left\{\begin{matrix}\\s=\frac{\sqrt{29}-5}{2}\text{; }s=\frac{-\sqrt{29}-5}{2}\text{, }&\text{unconditionally}\\s\in \mathrm{R}\text{, }&d=0\end{matrix}\right.$$