Solve mu=tau/du/dy

$$\mu = \frac { \tau } { d u / d y }$$

Solve for u (complex solution)

$$\left\{\begin{matrix}u=\frac{\tau }{y\mu }\text{, }&\tau \neq 0\text{ and }y\neq 0\text{ and }\mu \neq 0\text{ and }d\neq 0\\u\neq 0\text{, }&\mu =0\text{ and }\tau =0\text{ and }y\neq 0\text{ and }d\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Cancel out d in both numerator and denominator.

$$\mu =\frac{\tau }{uy}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{\tau }{uy}=\mu$$

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

$$\tau =\mu uy$$

Reorder the terms.

$$\tau =uy\mu$$

Swap sides so that all variable terms are on the left hand side.

$$uy\mu =\tau$$

The equation is in standard form.

$$y\mu u=\tau$$

Divide both sides by \mu y.

$$\frac{y\mu u}{y\mu }=\frac{\tau }{y\mu }$$

Dividing by \mu y undoes the multiplication by \mu y.

$$u=\frac{\tau }{y\mu }$$

Variable u cannot be equal to 0.

$$u=\frac{\tau }{y\mu }\text{, }u\neq 0$$

Solve for u

$$\left\{\begin{matrix}u=\frac{\tau }{y\mu }\text{, }&y\neq 0\text{ and }\mu \neq 0\text{ and }\tau \neq 0\text{ and }d\neq 0\\u\neq 0\text{, }&\mu =0\text{ and }\tau =0\text{ and }y\neq 0\text{ and }d\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Cancel out d in both numerator and denominator.

$$\mu =\frac{\tau }{uy}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{\tau }{uy}=\mu$$

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

$$\tau =\mu uy$$

Reorder the terms.

$$\tau =uy\mu$$

Swap sides so that all variable terms are on the left hand side.

$$uy\mu =\tau$$

The equation is in standard form.

$$y\mu u=\tau$$

Divide both sides by \mu y.

$$\frac{y\mu u}{y\mu }=\frac{\tau }{y\mu }$$

Dividing by \mu y undoes the multiplication by \mu y.

$$u=\frac{\tau }{y\mu }$$

Variable u cannot be equal to 0.

$$u=\frac{\tau }{y\mu }\text{, }u\neq 0$$

Solve for d (complex solution)

$$d\neq 0$$

$$\left(\mu =0\text{ and }\tau =0\text{ and }y\neq 0\text{ and }u\neq 0\right)\text{ or }\left(u=\frac{\tau }{y\mu }\text{ and }y\neq 0\text{ and }\mu \neq 0\text{ and }\tau \neq 0\right)$$

Solve for d

$$d\in \mathrm{R}$$

$$\left(u=\frac{\tau }{y\mu }\text{ and }y\neq 0\text{ and }\mu \neq 0\text{ and }\tau \neq 0\right)\text{ or }\left(\mu =0\text{ and }\tau =0\text{ and }y\neq 0\text{ and }u\neq 0\right)$$