Solve for a
\left\{\begin{matrix}a=\frac{c}{5b+7}\text{, }&b\neq -\frac{7}{5}\\a\in \mathrm{R}\text{, }&c=0\text{ and }b=-\frac{7}{5}\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=\frac{c}{5a}-\frac{7}{5}\text{, }&a\neq 0\\b\in \mathrm{R}\text{, }&c=0\text{ and }a=0\end{matrix}\right.
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7a+5ab=c
Swap sides so that all variable terms are on the left hand side.
\left(7+5b\right)a=c
Combine all terms containing a.
\left(5b+7\right)a=c
The equation is in standard form.
\frac{\left(5b+7\right)a}{5b+7}=\frac{c}{5b+7}
Divide both sides by 7+5b.
a=\frac{c}{5b+7}
Dividing by 7+5b undoes the multiplication by 7+5b.
7a+5ab=c
Swap sides so that all variable terms are on the left hand side.
5ab=c-7a
Subtract 7a from both sides.
\frac{5ab}{5a}=\frac{c-7a}{5a}
Divide both sides by 5a.
b=\frac{c-7a}{5a}
Dividing by 5a undoes the multiplication by 5a.
b=\frac{c}{5a}-\frac{7}{5}
Divide c-7a by 5a.
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