Solve for a
\left\{\begin{matrix}a=\frac{A+c}{5b+4c}\text{, }&b\neq -\frac{4c}{5}\\a\in \mathrm{R}\text{, }&b=-\frac{4c}{5}\text{ and }A=-c\end{matrix}\right.
Solve for A
A=-\left(c-4ac-5ab\right)
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5ab+4ac-c=A
Swap sides so that all variable terms are on the left hand side.
5ab+4ac=A+c
Add c to both sides.
\left(5b+4c\right)a=A+c
Combine all terms containing a.
\frac{\left(5b+4c\right)a}{5b+4c}=\frac{A+c}{5b+4c}
Divide both sides by 5b+4c.
a=\frac{A+c}{5b+4c}
Dividing by 5b+4c undoes the multiplication by 5b+4c.
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