Solve for c
\left\{\begin{matrix}c=\frac{\sqrt{2}a}{10m}\text{, }&m\neq 0\\c\in \mathrm{R}\text{, }&a=0\text{ and }m=0\end{matrix}\right.
Solve for a
a=5\sqrt{2}cm
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5\sqrt{2}cm=a
Swap sides so that all variable terms are on the left hand side.
5\sqrt{2}mc=a
The equation is in standard form.
\frac{5\sqrt{2}mc}{5\sqrt{2}m}=\frac{a}{5\sqrt{2}m}
Divide both sides by 5\sqrt{2}m.
c=\frac{a}{5\sqrt{2}m}
Dividing by 5\sqrt{2}m undoes the multiplication by 5\sqrt{2}m.
c=\frac{\sqrt{2}a}{10m}
Divide a by 5\sqrt{2}m.
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