Solve ABCd+ubed=e

$$A B C d + u b e d = e$$

Solve for A (complex solution)

$$\left\{\begin{matrix}A=-\frac{e\left(bdu-1\right)}{BCd}\text{, }&d\neq 0\text{ and }C\neq 0\text{ and }B\neq 0\\A\in \mathrm{C}\text{, }&d=\frac{1}{bu}\text{ and }b\neq 0\text{ and }u\neq 0\text{ and }\left(C=0\text{ or }B=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ubed from both sides.

$$ABCd=e-ubed$$

Reorder the terms.

$$ABCd=-ebdu+e$$

The equation is in standard form.

$$BCdA=e-ebdu$$

Divide both sides by BCd.

$$\frac{BCdA}{BCd}=\frac{e-ebdu}{BCd}$$

Dividing by BCd undoes the multiplication by BCd.

$$A=\frac{e-ebdu}{BCd}$$

Divide -ebdu+e by BCd.

$$A=\frac{e\left(1-bdu\right)}{BCd}$$

Solve for B (complex solution)

$$\left\{\begin{matrix}B=-\frac{e\left(bdu-1\right)}{ACd}\text{, }&d\neq 0\text{ and }C\neq 0\text{ and }A\neq 0\\B\in \mathrm{C}\text{, }&d=\frac{1}{bu}\text{ and }b\neq 0\text{ and }u\neq 0\text{ and }\left(C=0\text{ or }A=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ubed from both sides.

$$ABCd=e-ubed$$

Reorder the terms.

$$ABCd=-ebdu+e$$

The equation is in standard form.

$$ACdB=e-ebdu$$

Divide both sides by ACd.

$$\frac{ACdB}{ACd}=\frac{e-ebdu}{ACd}$$

Dividing by ACd undoes the multiplication by ACd.

$$B=\frac{e-ebdu}{ACd}$$

Divide -ebdu+e by ACd.

$$B=\frac{e\left(1-bdu\right)}{ACd}$$

Solve for A

$$\left\{\begin{matrix}A=-\frac{e\left(bdu-1\right)}{BCd}\text{, }&d\neq 0\text{ and }C\neq 0\text{ and }B\neq 0\\A\in \mathrm{R}\text{, }&\left(b=\frac{1}{du}\text{ and }u\neq 0\text{ and }d\neq 0\text{ and }C=0\right)\text{ or }\left(d=\frac{1}{bu}\text{ and }u\neq 0\text{ and }B=0\text{ and }C\neq 0\text{ and }b\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ubed from both sides.

$$ABCd=e-ubed$$

Reorder the terms.

$$ABCd=-ebdu+e$$

The equation is in standard form.

$$BCdA=e-ebdu$$

Divide both sides by BCd.

$$\frac{BCdA}{BCd}=\frac{e-ebdu}{BCd}$$

Dividing by BCd undoes the multiplication by BCd.

$$A=\frac{e-ebdu}{BCd}$$

Divide -ebdu+e by BCd.

$$A=\frac{e\left(1-bdu\right)}{BCd}$$

Solve for B

$$\left\{\begin{matrix}B=-\frac{e\left(bdu-1\right)}{ACd}\text{, }&d\neq 0\text{ and }C\neq 0\text{ and }A\neq 0\\B\in \mathrm{R}\text{, }&\left(b=\frac{1}{du}\text{ and }u\neq 0\text{ and }d\neq 0\text{ and }C=0\right)\text{ or }\left(d=\frac{1}{bu}\text{ and }u\neq 0\text{ and }A=0\text{ and }C\neq 0\text{ and }b\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ubed from both sides.

$$ABCd=e-ubed$$

Reorder the terms.

$$ABCd=-ebdu+e$$

The equation is in standard form.

$$ACdB=e-ebdu$$

Divide both sides by ACd.

$$\frac{ACdB}{ACd}=\frac{e-ebdu}{ACd}$$

Dividing by ACd undoes the multiplication by ACd.

$$B=\frac{e-ebdu}{ACd}$$

Divide -ebdu+e by ACd.

$$B=\frac{e\left(1-bdu\right)}{ACd}$$