Solve AC=DE*BD/AD

$$A C = \frac { D E \cdot B D } { A D }$$

Solve for B (complex solution)

$$\left\{\begin{matrix}B=\frac{CA^{2}}{DE}\text{, }&E\neq 0\text{ and }A\neq 0\text{ and }D\neq 0\\B\in \mathrm{C}\text{, }&C=0\text{ and }E=0\text{ and }A\neq 0\text{ and }D\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by AD.

$$ACAD=DEBD$$

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

$$ACAD=D^{2}EB$$

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

$$A^{2}CD=D^{2}EB$$

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

$$D^{2}EB=A^{2}CD$$

The equation is in standard form.

$$ED^{2}B=CDA^{2}$$

Divide both sides by D^{2}E.

$$\frac{ED^{2}B}{ED^{2}}=\frac{CDA^{2}}{ED^{2}}$$

Dividing by D^{2}E undoes the multiplication by D^{2}E.

$$B=\frac{CDA^{2}}{ED^{2}}$$

Divide A^{2}CD by D^{2}E.

$$B=\frac{CA^{2}}{DE}$$

Solve for B

$$\left\{\begin{matrix}B=\frac{CA^{2}}{DE}\text{, }&E\neq 0\text{ and }A\neq 0\text{ and }D\neq 0\\B\in \mathrm{R}\text{, }&C=0\text{ and }E=0\text{ and }A\neq 0\text{ and }D\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by AD.

$$ACAD=DEBD$$

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

$$ACAD=D^{2}EB$$

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

$$A^{2}CD=D^{2}EB$$

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

$$D^{2}EB=A^{2}CD$$

The equation is in standard form.

$$ED^{2}B=CDA^{2}$$

Divide both sides by D^{2}E.

$$\frac{ED^{2}B}{ED^{2}}=\frac{CDA^{2}}{ED^{2}}$$

Dividing by D^{2}E undoes the multiplication by D^{2}E.

$$B=\frac{CDA^{2}}{ED^{2}}$$

Divide A^{2}CD by D^{2}E.

$$B=\frac{CA^{2}}{DE}$$

Solve for A (complex solution)

$$\left\{\begin{matrix}A=-C^{-\frac{1}{2}}\sqrt{B}\sqrt{D}\sqrt{E}\text{; }A=C^{-\frac{1}{2}}\sqrt{B}\sqrt{D}\sqrt{E}\text{, }&D\neq 0\text{ and }B\neq 0\text{ and }E\neq 0\text{ and }C\neq 0\\A\neq 0\text{, }&\left(B=0\text{ or }E=0\right)\text{ and }C=0\text{ and }D\neq 0\end{matrix}\right.$$