bc - df = gh
Solve for b (complex solution)
\left\{\begin{matrix}b=\frac{df+gh}{c}\text{, }&c\neq 0\\b\in \mathrm{C}\text{, }&\left(d=-\frac{gh}{f}\text{ and }f\neq 0\text{ and }c=0\right)\text{ or }\left(h=0\text{ and }f=0\text{ and }c=0\right)\text{ or }\left(g=0\text{ and }f=0\text{ and }c=0\right)\end{matrix}\right.
Solve for c (complex solution)
\left\{\begin{matrix}c=\frac{df+gh}{b}\text{, }&b\neq 0\\c\in \mathrm{C}\text{, }&\left(d=-\frac{gh}{f}\text{ and }f\neq 0\text{ and }b=0\right)\text{ or }\left(h=0\text{ and }f=0\text{ and }b=0\right)\text{ or }\left(g=0\text{ and }f=0\text{ and }b=0\right)\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=\frac{df+gh}{c}\text{, }&c\neq 0\\b\in \mathrm{R}\text{, }&\left(d=-\frac{gh}{f}\text{ and }f\neq 0\text{ and }c=0\right)\text{ or }\left(h=0\text{ and }f=0\text{ and }c=0\right)\text{ or }\left(g=0\text{ and }f=0\text{ and }c=0\right)\end{matrix}\right.
Solve for c
\left\{\begin{matrix}c=\frac{df+gh}{b}\text{, }&b\neq 0\\c\in \mathrm{R}\text{, }&\left(d=-\frac{gh}{f}\text{ and }f\neq 0\text{ and }b=0\right)\text{ or }\left(h=0\text{ and }f=0\text{ and }b=0\right)\text{ or }\left(g=0\text{ and }f=0\text{ and }b=0\right)\end{matrix}\right.
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bc=gh+df
Add df to both sides.
cb=df+gh
The equation is in standard form.
\frac{cb}{c}=\frac{df+gh}{c}
Divide both sides by c.
b=\frac{df+gh}{c}
Dividing by c undoes the multiplication by c.
bc=gh+df
Add df to both sides.
bc=df+gh
The equation is in standard form.
\frac{bc}{b}=\frac{df+gh}{b}
Divide both sides by b.
c=\frac{df+gh}{b}
Dividing by b undoes the multiplication by b.
bc=gh+df
Add df to both sides.
cb=df+gh
The equation is in standard form.
\frac{cb}{c}=\frac{df+gh}{c}
Divide both sides by c.
b=\frac{df+gh}{c}
Dividing by c undoes the multiplication by c.
bc=gh+df
Add df to both sides.
bc=df+gh
The equation is in standard form.
\frac{bc}{b}=\frac{df+gh}{b}
Divide both sides by b.
c=\frac{df+gh}{b}
Dividing by b undoes the multiplication by b.
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