Solve AB+BC+CD+DA=AC+BC

$$A B + B C + C D + D A = A C + B C$$

Solve for A

$$\left\{\begin{matrix}A=-\frac{CD}{B-C+D}\text{, }&B\neq C-D\\A\in \mathrm{R}\text{, }&\left(C=0\text{ and }B=-D\right)\text{ or }\left(D=0\text{ and }B=C\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract AC from both sides.

$$AB+BC+CD+DA-AC=BC$$

Subtract BC from both sides.

$$AB+CD+DA-AC=BC-BC$$

Combine BC and -BC to get 0.

$$AB+CD+DA-AC=0$$

Subtract CD from both sides. Anything subtracted from zero gives its negation.

$$AB+DA-AC=-CD$$

Reorder the terms.

$$AB-AC+AD=-CD$$

Combine all terms containing A.

$$\left(B-C+D\right)A=-CD$$

Divide both sides by B-C+D.

$$\frac{\left(B-C+D\right)A}{B-C+D}=-\frac{CD}{B-C+D}$$

Dividing by B-C+D undoes the multiplication by B-C+D.

$$A=-\frac{CD}{B-C+D}$$

Solve for B

$$\left\{\begin{matrix}B=-\frac{CD}{A}+C-D\text{, }&A\neq 0\\B\in \mathrm{R}\text{, }&A=0\text{ and }\left(D=0\text{ or }C=0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract BC from both sides.

$$AB+BC+CD+DA-BC=AC$$

Combine BC and -BC to get 0.

$$AB+CD+DA=AC$$

Subtract CD from both sides.

$$AB+DA=AC-CD$$

Subtract DA from both sides.

$$AB=AC-CD-DA$$

The equation is in standard form.

$$AB=AC-AD-CD$$

Divide both sides by A.

$$\frac{AB}{A}=\frac{AC-AD-CD}{A}$$

Dividing by A undoes the multiplication by A.

$$B=\frac{AC-AD-CD}{A}$$

Divide AC-CD-DA by A.

$$B=-\frac{CD}{A}+C-D$$