Solve mv_{2}-mv_{1}=ft,v_{2}

$$m v _ { 2 } - m v _ { 1 } = f t , v _ { 2 }$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=\frac{m\left(v_{2}-v_{1}\right)}{t}\text{, }&t\neq 0\\f\in \mathrm{C}\text{, }&\left(m=0\text{ or }v_{2}=v_{1}\right)\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ft=mv_{2}-mv_{1}$$

The equation is in standard form.

$$tf=mv_{2}-mv_{1}$$

Divide both sides by t.

$$\frac{tf}{t}=\frac{m\left(v_{2}-v_{1}\right)}{t}$$

Dividing by t undoes the multiplication by t.

$$f=\frac{m\left(v_{2}-v_{1}\right)}{t}$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{ft}{v_{2}-v_{1}}\text{, }&v_{2}\neq v_{1}\\m\in \mathrm{C}\text{, }&\left(t=0\text{ or }f=0\right)\text{ and }v_{2}=v_{1}\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine all terms containing m.

$$\left(v_{2}-v_{1}\right)m=ft$$

Divide both sides by v_{2}-v_{1}.

$$\frac{\left(v_{2}-v_{1}\right)m}{v_{2}-v_{1}}=\frac{ft}{v_{2}-v_{1}}$$

Dividing by v_{2}-v_{1} undoes the multiplication by v_{2}-v_{1}.

$$m=\frac{ft}{v_{2}-v_{1}}$$

Solve for f

$$\left\{\begin{matrix}f=\frac{m\left(v_{2}-v_{1}\right)}{t}\text{, }&t\neq 0\\f\in \mathrm{R}\text{, }&\left(m=0\text{ or }v_{2}=v_{1}\right)\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ft=mv_{2}-mv_{1}$$

The equation is in standard form.

$$tf=mv_{2}-mv_{1}$$

Divide both sides by t.

$$\frac{tf}{t}=\frac{m\left(v_{2}-v_{1}\right)}{t}$$

Dividing by t undoes the multiplication by t.

$$f=\frac{m\left(v_{2}-v_{1}\right)}{t}$$

Solve for m

$$\left\{\begin{matrix}m=\frac{ft}{v_{2}-v_{1}}\text{, }&v_{2}\neq v_{1}\\m\in \mathrm{R}\text{, }&\left(t=0\text{ or }f=0\right)\text{ and }v_{2}=v_{1}\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine all terms containing m.

$$\left(v_{2}-v_{1}\right)m=ft$$

Divide both sides by v_{2}-v_{1}.

$$\frac{\left(v_{2}-v_{1}\right)m}{v_{2}-v_{1}}=\frac{ft}{v_{2}-v_{1}}$$

Dividing by v_{2}-v_{1} undoes the multiplication by v_{2}-v_{1}.

$$m=\frac{ft}{v_{2}-v_{1}}$$