Solve for q (complex solution)
\left\{\begin{matrix}q=\frac{xz+b}{xy}\text{, }&y\neq 0\text{ and }x\neq 0\\q\in \mathrm{C}\text{, }&\left(b=-xz\text{ and }y=0\right)\text{ or }\left(b=0\text{ and }x=0\text{ and }y\neq 0\right)\end{matrix}\right.
Solve for q
\left\{\begin{matrix}q=\frac{xz+b}{xy}\text{, }&y\neq 0\text{ and }x\neq 0\\q\in \mathrm{R}\text{, }&\left(b=-xz\text{ and }y=0\right)\text{ or }\left(b=0\text{ and }x=0\text{ and }y\neq 0\right)\end{matrix}\right.
Solve for b
b=x\left(qy-z\right)
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xyq=b+xz
Swap sides so that all variable terms are on the left hand side.
xyq=xz+b
The equation is in standard form.
\frac{xyq}{xy}=\frac{xz+b}{xy}
Divide both sides by xy.
q=\frac{xz+b}{xy}
Dividing by xy undoes the multiplication by xy.
xyq=b+xz
Swap sides so that all variable terms are on the left hand side.
xyq=xz+b
The equation is in standard form.
\frac{xyq}{xy}=\frac{xz+b}{xy}
Divide both sides by xy.
q=\frac{xz+b}{xy}
Dividing by xy undoes the multiplication by xy.
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