Solve for a (complex solution)
\left\{\begin{matrix}a=\frac{K}{9b+4}\text{, }&b\neq -\frac{4}{9}\\a\in \mathrm{C}\text{, }&K=0\text{ and }b=-\frac{4}{9}\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=\frac{K}{9b+4}\text{, }&b\neq -\frac{4}{9}\\a\in \mathrm{R}\text{, }&K=0\text{ and }b=-\frac{4}{9}\end{matrix}\right.
Solve for K
K=a\left(9b+4\right)
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4a+9ab=K
Swap sides so that all variable terms are on the left hand side.
\left(4+9b\right)a=K
Combine all terms containing a.
\left(9b+4\right)a=K
The equation is in standard form.
\frac{\left(9b+4\right)a}{9b+4}=\frac{K}{9b+4}
Divide both sides by 4+9b.
a=\frac{K}{9b+4}
Dividing by 4+9b undoes the multiplication by 4+9b.
4a+9ab=K
Swap sides so that all variable terms are on the left hand side.
\left(4+9b\right)a=K
Combine all terms containing a.
\left(9b+4\right)a=K
The equation is in standard form.
\frac{\left(9b+4\right)a}{9b+4}=\frac{K}{9b+4}
Divide both sides by 4+9b.
a=\frac{K}{9b+4}
Dividing by 4+9b undoes the multiplication by 4+9b.
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