Solve (10mM)(v.1)=(1.0mm)(10m)

$$( 10 m M ) ( v .1 ) = ( 1.0 m m ) ( 10 m )$$

Solve for M

$$\left\{\begin{matrix}M=\frac{10m^{2}}{v}\text{, }&v\neq 0\\M\in \mathrm{R}\text{, }&m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Cancel out 10 on both sides.

$$mMv\times 0.1=1mmm$$

Multiply m and m to get m^{2}.

$$mMv\times 0.1=1m^{2}m$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$mMv\times 0.1=1m^{3}$$

Reorder the terms.

$$0.1Mmv=m^{3}$$

The equation is in standard form.

$$\frac{mv}{10}M=m^{3}$$

Divide both sides by 0.1mv.

$$\frac{10\times \frac{mv}{10}M}{mv}=\frac{10m^{3}}{mv}$$

Dividing by 0.1mv undoes the multiplication by 0.1mv.

$$M=\frac{10m^{3}}{mv}$$

Divide m^{3} by 0.1mv.

$$M=\frac{10m^{2}}{v}$$

Solve for m

$$\left\{\begin{matrix}\\m=0\text{, }&\text{unconditionally}\\m=\frac{\sqrt{10Mv}}{10}\text{; }m=-\frac{\sqrt{10Mv}}{10}\text{, }&\left(v\geq 0\text{ and }M\geq 0\right)\text{ or }\left(M\leq 0\text{ and }v\leq 0\right)\end{matrix}\right.$$