Solve AD^2=AB*AF

$$AD ^ { 2 } = AB \times AF$$

Solve for B

$$\left\{\begin{matrix}B=\frac{D^{2}}{AF}\text{, }&F\neq 0\text{ and }A\neq 0\\B\in \mathrm{R}\text{, }&\left(D=0\text{ and }F=0\right)\text{ or }A=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$AD^{2}=A^{2}BF$$

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

$$A^{2}BF=AD^{2}$$

The equation is in standard form.

$$FA^{2}B=AD^{2}$$

Divide both sides by A^{2}F.

$$\frac{FA^{2}B}{FA^{2}}=\frac{AD^{2}}{FA^{2}}$$

Dividing by A^{2}F undoes the multiplication by A^{2}F.

$$B=\frac{AD^{2}}{FA^{2}}$$

Divide AD^{2} by A^{2}F.

$$B=\frac{D^{2}}{AF}$$

Solve for A

$$\left\{\begin{matrix}\\A=0\text{, }&\text{unconditionally}\\A=\frac{D^{2}}{BF}\text{, }&F\neq 0\text{ and }B\neq 0\\A\in \mathrm{R}\text{, }&\left(B=0\text{ or }F=0\right)\text{ and }D=0\end{matrix}\right.$$