Solve for A
\left\{\begin{matrix}\\A=0\text{, }&\text{unconditionally}\\A\in \mathrm{R}\text{, }&|D|=\sqrt{7}|B|\end{matrix}\right.
Solve for B
\left\{\begin{matrix}\\B=\frac{\sqrt{7}D}{7}\text{; }B=-\frac{\sqrt{7}D}{7}\text{, }&\text{unconditionally}\\B\in \mathrm{R}\text{, }&A=0\end{matrix}\right.
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AD^{2}-7AB^{2}=0
Subtract 7AB^{2} from both sides.
\left(D^{2}-7B^{2}\right)A=0
Combine all terms containing A.
A=0
Divide 0 by D^{2}-7B^{2}.
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