Solve for m
m=\frac{2e}{v^{2}}
v\neq 0
Solve for v
v=\sqrt{\frac{2e}{m}}
v=-\sqrt{\frac{2e}{m}}\text{, }m>0
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\frac{1}{2}mv^{2}=e
Swap sides so that all variable terms are on the left hand side.
\frac{v^{2}}{2}m=e
The equation is in standard form.
\frac{2\times \frac{v^{2}}{2}m}{v^{2}}=\frac{2e}{v^{2}}
Divide both sides by \frac{1}{2}v^{2}.
m=\frac{2e}{v^{2}}
Dividing by \frac{1}{2}v^{2} undoes the multiplication by \frac{1}{2}v^{2}.
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