Solve ES=Mv^2/2

$$E S = \frac { M v ^ { 2 } } { 2 }$$

Solve for E

$$\left\{\begin{matrix}E=\frac{Mv^{2}}{2S}\text{, }&S\neq 0\\E\in \mathrm{R}\text{, }&\left(M=0\text{ or }v=0\right)\text{ and }S=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2ES=Mv^{2}$$

The equation is in standard form.

$$2SE=Mv^{2}$$

Divide both sides by 2S.

$$\frac{2SE}{2S}=\frac{Mv^{2}}{2S}$$

Dividing by 2S undoes the multiplication by 2S.

$$E=\frac{Mv^{2}}{2S}$$

Solve for M

$$\left\{\begin{matrix}M=\frac{2ES}{v^{2}}\text{, }&v\neq 0\\M\in \mathrm{R}\text{, }&\left(E=0\text{ or }S=0\right)\text{ and }v=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2ES=Mv^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$Mv^{2}=2ES$$

The equation is in standard form.

$$v^{2}M=2ES$$

Divide both sides by v^{2}.

$$\frac{v^{2}M}{v^{2}}=\frac{2ES}{v^{2}}$$

Dividing by v^{2} undoes the multiplication by v^{2}.

$$M=\frac{2ES}{v^{2}}$$