Solve (10mM)(v1)=(10mm)(10m)

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

Solve for M (complex solution)

$$\left\{\begin{matrix}M=\frac{10m^{2}}{v_{1}}\text{, }&v_{1}\neq 0\\M\in \mathrm{C}\text{, }&m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Cancel out 10 on both sides.

$$mMv_{1}=mm\times 10m$$

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

$$mMv_{1}=m^{2}\times 10m$$

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

$$mMv_{1}=m^{3}\times 10$$

The equation is in standard form.

$$mv_{1}M=10m^{3}$$

Divide both sides by mv_{1}.

$$\frac{mv_{1}M}{mv_{1}}=\frac{10m^{3}}{mv_{1}}$$

Dividing by mv_{1} undoes the multiplication by mv_{1}.

$$M=\frac{10m^{3}}{mv_{1}}$$

Divide 10m^{3} by mv_{1}.

$$M=\frac{10m^{2}}{v_{1}}$$

Solve for M

$$\left\{\begin{matrix}M=\frac{10m^{2}}{v_{1}}\text{, }&v_{1}\neq 0\\M\in \mathrm{R}\text{, }&m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Cancel out 10 on both sides.

$$mMv_{1}=mm\times 10m$$

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

$$mMv_{1}=m^{2}\times 10m$$

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

$$mMv_{1}=m^{3}\times 10$$

The equation is in standard form.

$$mv_{1}M=10m^{3}$$

Divide both sides by mv_{1}.

$$\frac{mv_{1}M}{mv_{1}}=\frac{10m^{3}}{mv_{1}}$$

Dividing by mv_{1} undoes the multiplication by mv_{1}.

$$M=\frac{10m^{3}}{mv_{1}}$$

Divide 10m^{3} by mv_{1}.

$$M=\frac{10m^{2}}{v_{1}}$$

Solve for m (complex solution)

$$m=\frac{\sqrt{v_{1}}\sqrt{10M}}{10}$$

$$m=0$$

$$m=-\frac{\sqrt{v_{1}}\sqrt{10M}}{10}$$

Solve for m

$$\left\{\begin{matrix}\\m=0\text{, }&\text{unconditionally}\\m=\frac{\sqrt{10Mv_{1}}}{10}\text{; }m=-\frac{\sqrt{10Mv_{1}}}{10}\text{, }&\left(v_{1}\geq 0\text{ and }M\geq 0\right)\text{ or }\left(M\leq 0\text{ and }v_{1}\leq 0\right)\end{matrix}\right.$$