Solve AC=DE*BD/DeltaD

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

Solve for A (complex solution)

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

Steps for Solving Linear Equation

Multiply both sides of the equation by D\Delta .

$$ACD\Delta =DEBD$$

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

$$ACD\Delta =D^{2}EB$$

The equation is in standard form.

$$CD\Delta A=BED^{2}$$

Divide both sides by CD\Delta .

$$\frac{CD\Delta A}{CD\Delta }=\frac{BED^{2}}{CD\Delta }$$

Dividing by CD\Delta undoes the multiplication by CD\Delta .

$$A=\frac{BED^{2}}{CD\Delta }$$

Divide D^{2}EB by CD\Delta .

$$A=\frac{BDE}{C\Delta }$$

Solve for B (complex solution)

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

Steps for Solving Linear Equation

Multiply both sides of the equation by D\Delta .

$$ACD\Delta =DEBD$$

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

$$ACD\Delta =D^{2}EB$$

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

$$D^{2}EB=ACD\Delta$$

The equation is in standard form.

$$ED^{2}B=ACD\Delta$$

Divide both sides by D^{2}E.

$$\frac{ED^{2}B}{ED^{2}}=\frac{ACD\Delta }{ED^{2}}$$

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

$$B=\frac{ACD\Delta }{ED^{2}}$$

Divide ACD\Delta by D^{2}E.

$$B=\frac{AC\Delta }{DE}$$

Solve for A

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

Steps for Solving Linear Equation

Multiply both sides of the equation by D\Delta .

$$ACD\Delta =DEBD$$

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

$$ACD\Delta =D^{2}EB$$

The equation is in standard form.

$$CD\Delta A=BED^{2}$$

Divide both sides by CD\Delta .

$$\frac{CD\Delta A}{CD\Delta }=\frac{BED^{2}}{CD\Delta }$$

Dividing by CD\Delta undoes the multiplication by CD\Delta .

$$A=\frac{BED^{2}}{CD\Delta }$$

Divide D^{2}EB by CD\Delta .

$$A=\frac{BDE}{C\Delta }$$

Solve for B

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

Steps for Solving Linear Equation

Multiply both sides of the equation by D\Delta .

$$ACD\Delta =DEBD$$

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

$$ACD\Delta =D^{2}EB$$

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

$$D^{2}EB=ACD\Delta$$

The equation is in standard form.

$$ED^{2}B=ACD\Delta$$

Divide both sides by D^{2}E.

$$\frac{ED^{2}B}{ED^{2}}=\frac{ACD\Delta }{ED^{2}}$$

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

$$B=\frac{ACD\Delta }{ED^{2}}$$

Divide ACD\Delta by D^{2}E.

$$B=\frac{AC\Delta }{DE}$$