Solve operatorname{ar}(DeltaAOB)=operatorname{ar}(DeltaAOD)

$$\operatorname { ar } ( \Delta A O B ) = \operatorname { ar } ( \Delta A O D )$$

Solve for A

$$\left\{\begin{matrix}\\A=0\text{, }&\text{unconditionally}\\A\in \mathrm{R}\text{, }&B=D\text{ or }O=0\text{ or }\Delta =0\text{ or }r=0\text{ or }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract ar\Delta AOD from both sides.

$$ar\Delta AOB-ar\Delta AOD=0$$

Reorder the terms.

$$ABOar\Delta -ADOar\Delta =0$$

Combine all terms containing A.

$$\left(BOar\Delta -DOar\Delta \right)A=0$$

Divide 0 by BOar\Delta -DOar\Delta .

$$A=0$$

Solve for B

$$\left\{\begin{matrix}\\B=D\text{, }&\text{unconditionally}\\B\in \mathrm{R}\text{, }&O=0\text{ or }A=0\text{ or }\Delta =0\text{ or }r=0\text{ or }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$AOar\Delta B=ADOar\Delta$$

Divide both sides by ar\Delta AO.

$$\frac{AOar\Delta B}{AOar\Delta }=\frac{ADOar\Delta }{AOar\Delta }$$

Dividing by ar\Delta AO undoes the multiplication by ar\Delta AO.

$$B=\frac{ADOar\Delta }{AOar\Delta }$$

Divide ar\Delta AOD by ar\Delta AO.

$$B=D$$