Solve w=t^2(2u-3v)/5s

$$w = \frac { t ^ { 2 } ( 2 u - 3 v ) } { 5 s }$$

Solve for s

$$\left\{\begin{matrix}s=\frac{\left(2u-3v\right)t^{2}}{5w}\text{, }&u\neq \frac{3v}{2}\text{ and }t\neq 0\text{ and }w\neq 0\\s\neq 0\text{, }&\left(t=0\text{ or }u=\frac{3v}{2}\right)\text{ and }w=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable s cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5s.

$$w\times 5s=t^{2}\left(2u-3v\right)$$

Use the distributive property to multiply t^{2} by 2u-3v.

$$w\times 5s=2t^{2}u-3t^{2}v$$

The equation is in standard form.

$$5ws=2ut^{2}-3vt^{2}$$

Divide both sides by 5w.

$$\frac{5ws}{5w}=\frac{\left(2u-3v\right)t^{2}}{5w}$$

Dividing by 5w undoes the multiplication by 5w.

$$s=\frac{\left(2u-3v\right)t^{2}}{5w}$$

Variable s cannot be equal to 0.

$$s=\frac{\left(2u-3v\right)t^{2}}{5w}\text{, }s\neq 0$$

Solve for t (complex solution)

$$\left\{\begin{matrix}t=-\left(2u-3v\right)^{-\frac{1}{2}}\sqrt{w}\sqrt{5s}\text{; }t=\left(2u-3v\right)^{-\frac{1}{2}}\sqrt{w}\sqrt{5s}\text{, }&s\neq 0\text{ and }u\neq \frac{3v}{2}\\t\in \mathrm{C}\text{, }&w=0\text{ and }u=\frac{3v}{2}\text{ and }s\neq 0\end{matrix}\right.$$

Solve for t

$$\left\{\begin{matrix}t=\sqrt{\frac{5sw}{2u-3v}}\text{; }t=-\sqrt{\frac{5sw}{2u-3v}}\text{, }&\left(s>0\text{ or }u>\frac{3v}{2}\text{ or }w\geq 0\right)\text{ and }u\neq \frac{3v}{2}\text{ and }\left(s>0\text{ or }w\leq 0\text{ or }u<\frac{3v}{2}\right)\text{ and }\left(u>\frac{3v}{2}\text{ or }w\leq 0\text{ or }s<0\right)\text{ and }s\neq 0\text{ and }\left(u<\frac{3v}{2}\text{ or }s<0\text{ or }w\geq 0\right)\\t\in \mathrm{R}\text{, }&w=0\text{ and }u=\frac{3v}{2}\text{ and }s\neq 0\end{matrix}\right.$$