Solve for B
\left\{\begin{matrix}\\B=0\text{, }&\text{unconditionally}\\B\in \mathrm{R}\text{, }&G=DK\end{matrix}\right.
Solve for D
\left\{\begin{matrix}D=\frac{G}{K}\text{, }&K\neq 0\\D\in \mathrm{R}\text{, }&B=0\text{ or }\left(G=0\text{ and }K=0\right)\end{matrix}\right.
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GB-DKB=0
Subtract DKB from both sides.
-BDK+BG=0
Reorder the terms.
\left(-DK+G\right)B=0
Combine all terms containing B.
\left(G-DK\right)B=0
The equation is in standard form.
B=0
Divide 0 by G-DK.
DKB=GB
Swap sides so that all variable terms are on the left hand side.
BKD=BG
The equation is in standard form.
\frac{BKD}{BK}=\frac{BG}{BK}
Divide both sides by KB.
D=\frac{BG}{BK}
Dividing by KB undoes the multiplication by KB.
D=\frac{G}{K}
Divide GB by KB.
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