Solve t=r+k/3wt

$$t = r + \frac { k } { 3 } w t$$

Solve for k (complex solution)

$$\left\{\begin{matrix}k=-\frac{3\left(r-t\right)}{tw}\text{, }&t\neq 0\text{ and }w\neq 0\\k\in \mathrm{C}\text{, }&\left(t=r\text{ and }w=0\right)\text{ or }\left(t=0\text{ and }r=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Express \frac{k}{3}w as a single fraction.

$$t=r+\frac{kw}{3}t$$

Express \frac{kw}{3}t as a single fraction.

$$t=r+\frac{kwt}{3}$$

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

$$r+\frac{kwt}{3}=t$$

Subtract r from both sides.

$$\frac{kwt}{3}=t-r$$

Multiply both sides of the equation by 3.

$$kwt=3t-3r$$

The equation is in standard form.

$$twk=3t-3r$$

Divide both sides by wt.

$$\frac{twk}{tw}=\frac{3t-3r}{tw}$$

Dividing by wt undoes the multiplication by wt.

$$k=\frac{3t-3r}{tw}$$

Divide 3t-3r by wt.

$$k=\frac{3\left(t-r\right)}{tw}$$

Solve for k

$$\left\{\begin{matrix}k=-\frac{3\left(r-t\right)}{tw}\text{, }&t\neq 0\text{ and }w\neq 0\\k\in \mathrm{R}\text{, }&\left(t=r\text{ and }w=0\right)\text{ or }\left(t=0\text{ and }r=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Express \frac{k}{3}w as a single fraction.

$$t=r+\frac{kw}{3}t$$

Express \frac{kw}{3}t as a single fraction.

$$t=r+\frac{kwt}{3}$$

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

$$r+\frac{kwt}{3}=t$$

Subtract r from both sides.

$$\frac{kwt}{3}=t-r$$

Multiply both sides of the equation by 3.

$$kwt=3t-3r$$

The equation is in standard form.

$$twk=3t-3r$$

Divide both sides by wt.

$$\frac{twk}{tw}=\frac{3t-3r}{tw}$$

Dividing by wt undoes the multiplication by wt.

$$k=\frac{3t-3r}{tw}$$

Divide 3t-3r by wt.

$$k=\frac{3\left(t-r\right)}{tw}$$

Solve for r

$$r=-\frac{ktw}{3}+t$$