Solve r=a(bd)

$$r = a ( b d )$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{r}{bd}\text{, }&d\neq 0\text{ and }b\neq 0\\a\in \mathrm{C}\text{, }&\left(d=0\text{ or }b=0\right)\text{ and }r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$abd=r$$

The equation is in standard form.

$$bda=r$$

Divide both sides by bd.

$$\frac{bda}{bd}=\frac{r}{bd}$$

Dividing by bd undoes the multiplication by bd.

$$a=\frac{r}{bd}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\frac{r}{ad}\text{, }&d\neq 0\text{ and }a\neq 0\\b\in \mathrm{C}\text{, }&\left(d=0\text{ or }a=0\right)\text{ and }r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$abd=r$$

The equation is in standard form.

$$adb=r$$

Divide both sides by ad.

$$\frac{adb}{ad}=\frac{r}{ad}$$

Dividing by ad undoes the multiplication by ad.

$$b=\frac{r}{ad}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{r}{bd}\text{, }&d\neq 0\text{ and }b\neq 0\\a\in \mathrm{R}\text{, }&\left(d=0\text{ or }b=0\right)\text{ and }r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$abd=r$$

The equation is in standard form.

$$bda=r$$

Divide both sides by bd.

$$\frac{bda}{bd}=\frac{r}{bd}$$

Dividing by bd undoes the multiplication by bd.

$$a=\frac{r}{bd}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{r}{ad}\text{, }&d\neq 0\text{ and }a\neq 0\\b\in \mathrm{R}\text{, }&\left(d=0\text{ or }a=0\right)\text{ and }r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$abd=r$$

The equation is in standard form.

$$adb=r$$

Divide both sides by ad.

$$\frac{adb}{ad}=\frac{r}{ad}$$

Dividing by ad undoes the multiplication by ad.

$$b=\frac{r}{ad}$$