Solve for a (complex solution)
\left\{\begin{matrix}a=\frac{m+bd}{c}\text{, }&c\neq 0\\a\in \mathrm{C}\text{, }&m=-bd\text{ and }c=0\end{matrix}\right.
Solve for b (complex solution)
\left\{\begin{matrix}b=\frac{ac-m}{d}\text{, }&d\neq 0\\b\in \mathrm{C}\text{, }&m=ac\text{ and }d=0\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=\frac{m+bd}{c}\text{, }&c\neq 0\\a\in \mathrm{R}\text{, }&m=-bd\text{ and }c=0\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=\frac{ac-m}{d}\text{, }&d\neq 0\\b\in \mathrm{R}\text{, }&m=ac\text{ and }d=0\end{matrix}\right.
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ac-bd=m
Swap sides so that all variable terms are on the left hand side.
ac=m+bd
Add bd to both sides.
ca=m+bd
The equation is in standard form.
\frac{ca}{c}=\frac{m+bd}{c}
Divide both sides by c.
a=\frac{m+bd}{c}
Dividing by c undoes the multiplication by c.
ac-bd=m
Swap sides so that all variable terms are on the left hand side.
-bd=m-ac
Subtract ac from both sides.
\left(-d\right)b=m-ac
The equation is in standard form.
\frac{\left(-d\right)b}{-d}=\frac{m-ac}{-d}
Divide both sides by -d.
b=\frac{m-ac}{-d}
Dividing by -d undoes the multiplication by -d.
b=-\frac{m-ac}{d}
Divide m-ac by -d.
ac-bd=m
Swap sides so that all variable terms are on the left hand side.
ac=m+bd
Add bd to both sides.
ca=m+bd
The equation is in standard form.
\frac{ca}{c}=\frac{m+bd}{c}
Divide both sides by c.
a=\frac{m+bd}{c}
Dividing by c undoes the multiplication by c.
ac-bd=m
Swap sides so that all variable terms are on the left hand side.
-bd=m-ac
Subtract ac from both sides.
\left(-d\right)b=m-ac
The equation is in standard form.
\frac{\left(-d\right)b}{-d}=\frac{m-ac}{-d}
Divide both sides by -d.
b=\frac{m-ac}{-d}
Dividing by -d undoes the multiplication by -d.
b=-\frac{m-ac}{d}
Divide m-ac by -d.
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