Solve VE=M(1-dt)

$$V E = M ( 1 - d t )$$

Solve for E (complex solution)

$$\left\{\begin{matrix}E=-\frac{M\left(dt-1\right)}{V}\text{, }&V\neq 0\\E\in \mathrm{C}\text{, }&\left(M=0\text{ and }V=0\right)\text{ or }\left(d=\frac{1}{t}\text{ and }t\neq 0\text{ and }V=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply M by 1-dt.

$$VE=M-Mdt$$

Divide both sides by V.

$$\frac{VE}{V}=\frac{M-Mdt}{V}$$

Dividing by V undoes the multiplication by V.

$$E=\frac{M-Mdt}{V}$$

Divide M-Mdt by V.

$$E=\frac{M\left(1-dt\right)}{V}$$

Solve for M (complex solution)

$$\left\{\begin{matrix}M=-\frac{EV}{dt-1}\text{, }&t=0\text{ or }d\neq \frac{1}{t}\\M\in \mathrm{C}\text{, }&\left(E=0\text{ or }V=0\right)\text{ and }d=\frac{1}{t}\text{ and }t\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply M by 1-dt.

$$VE=M-Mdt$$

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

$$M-Mdt=VE$$

Combine all terms containing M.

$$\left(1-dt\right)M=VE$$

The equation is in standard form.

$$\left(1-dt\right)M=EV$$

Divide both sides by 1-dt.

$$\frac{\left(1-dt\right)M}{1-dt}=\frac{EV}{1-dt}$$

Dividing by 1-dt undoes the multiplication by 1-dt.

$$M=\frac{EV}{1-dt}$$

Solve for E

$$\left\{\begin{matrix}E=-\frac{M\left(dt-1\right)}{V}\text{, }&V\neq 0\\E\in \mathrm{R}\text{, }&\left(M=0\text{ and }V=0\right)\text{ or }\left(d=\frac{1}{t}\text{ and }t\neq 0\text{ and }V=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply M by 1-dt.

$$VE=M-Mdt$$

Divide both sides by V.

$$\frac{VE}{V}=\frac{M-Mdt}{V}$$

Dividing by V undoes the multiplication by V.

$$E=\frac{M-Mdt}{V}$$

Divide M-Mdt by V.

$$E=\frac{M\left(1-dt\right)}{V}$$

Solve for M

$$\left\{\begin{matrix}M=-\frac{EV}{dt-1}\text{, }&t=0\text{ or }d\neq \frac{1}{t}\\M\in \mathrm{R}\text{, }&\left(E=0\text{ or }V=0\right)\text{ and }d=\frac{1}{t}\text{ and }t\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply M by 1-dt.

$$VE=M-Mdt$$

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

$$M-Mdt=VE$$

Combine all terms containing M.

$$\left(1-dt\right)M=VE$$

The equation is in standard form.

$$\left(1-dt\right)M=EV$$

Divide both sides by 1-dt.

$$\frac{\left(1-dt\right)M}{1-dt}=\frac{EV}{1-dt}$$

Dividing by 1-dt undoes the multiplication by 1-dt.

$$M=\frac{EV}{1-dt}$$