Solve s=10t+st^2

$$s = 10 t + s t ^ { 2 }$$

Solve for s (complex solution)

$$s=\frac{10t}{1-t^{2}}$$

$$t\neq 1\text{ and }t\neq -1$$

Steps for Solving Linear Equation

Subtract st^{2} from both sides.

$$s-st^{2}=10t$$

Reorder the terms.

$$-st^{2}+s=10t$$

Combine all terms containing s.

$$\left(-t^{2}+1\right)s=10t$$

The equation is in standard form.

$$\left(1-t^{2}\right)s=10t$$

Divide both sides by -t^{2}+1.

$$\frac{\left(1-t^{2}\right)s}{1-t^{2}}=\frac{10t}{1-t^{2}}$$

Dividing by -t^{2}+1 undoes the multiplication by -t^{2}+1.

$$s=\frac{10t}{1-t^{2}}$$

Solve for s

$$s=\frac{10t}{1-t^{2}}$$

$$|t|\neq 1$$

Steps for Solving Linear Equation

Subtract st^{2} from both sides.

$$s-st^{2}=10t$$

Reorder the terms.

$$-st^{2}+s=10t$$

Combine all terms containing s.

$$\left(-t^{2}+1\right)s=10t$$

The equation is in standard form.

$$\left(1-t^{2}\right)s=10t$$

Divide both sides by -t^{2}+1.

$$\frac{\left(1-t^{2}\right)s}{1-t^{2}}=\frac{10t}{1-t^{2}}$$

Dividing by -t^{2}+1 undoes the multiplication by -t^{2}+1.

$$s=\frac{10t}{1-t^{2}}$$

Solve for t

$$\left\{\begin{matrix}t=-\frac{\sqrt{s^{2}+25}+5}{s}\text{; }t=\frac{\sqrt{s^{2}+25}-5}{s}\text{, }&s\neq 0\\t=0\text{, }&s=0\end{matrix}\right.$$