Solve (t)v=mt/n-3

$$( t ) v = \frac { m t } { n } - 3$$

Solve for m

$$m=\frac{n\left(tv+3\right)}{t}$$

$$t\neq 0\text{ and }n\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by n.

$$tvn=mt+n\left(-3\right)$$

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

$$mt+n\left(-3\right)=tvn$$

Subtract n\left(-3\right) from both sides.

$$mt=tvn-n\left(-3\right)$$

Multiply -1 and -3 to get 3.

$$mt=tvn+3n$$

The equation is in standard form.

$$tm=ntv+3n$$

Divide both sides by t.

$$\frac{tm}{t}=\frac{n\left(tv+3\right)}{t}$$

Dividing by t undoes the multiplication by t.

$$m=\frac{n\left(tv+3\right)}{t}$$

Solve for n

$$\left\{\begin{matrix}n=\frac{mt}{tv+3}\text{, }&t\neq 0\text{ and }m\neq 0\text{ and }\left(v=0\text{ or }t\neq -\frac{3}{v}\right)\\n\neq 0\text{, }&t=-\frac{3}{v}\text{ and }m=0\text{ and }v\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$tvn=mt+n\left(-3\right)$$

Subtract n\left(-3\right) from both sides.

$$tvn-n\left(-3\right)=mt$$

Multiply -1 and -3 to get 3.

$$tvn+3n=mt$$

Combine all terms containing n.

$$\left(tv+3\right)n=mt$$

Divide both sides by tv+3.

$$\frac{\left(tv+3\right)n}{tv+3}=\frac{mt}{tv+3}$$

Dividing by tv+3 undoes the multiplication by tv+3.

$$n=\frac{mt}{tv+3}$$

Variable n cannot be equal to 0.

$$n=\frac{mt}{tv+3}\text{, }n\neq 0$$