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