Solve ABCD+ABED=EDCAD

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

Solve for A

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

Steps for Solving Linear Equation

Multiply D and D to get D^{2}.

$$ABCD+ABED=ED^{2}CA$$

Subtract ED^{2}CA from both sides.

$$ABCD+ABED-ED^{2}CA=0$$

Reorder the terms.

$$ABCD+ABDE-ACED^{2}=0$$

Combine all terms containing A.

$$\left(BCD+BDE-CED^{2}\right)A=0$$

Divide 0 by BCD+BDE-CED^{2}.

$$A=0$$

Solve for B

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

Steps for Solving Linear Equation

Multiply D and D to get D^{2}.

$$ABCD+ABED=ED^{2}CA$$

Combine all terms containing B.

$$\left(ACD+AED\right)B=ED^{2}CA$$

The equation is in standard form.

$$\left(ACD+ADE\right)B=ACED^{2}$$

Divide both sides by ACD+AED.

$$\frac{\left(ACD+ADE\right)B}{ACD+ADE}=\frac{ACED^{2}}{ACD+ADE}$$

Dividing by ACD+AED undoes the multiplication by ACD+AED.

$$B=\frac{ACED^{2}}{ACD+ADE}$$

Divide ED^{2}CA by ACD+AED.

$$B=\frac{CDE}{C+E}$$