Trying to do a physics problem but I can't understand the mathematical logic on why the term m cancels out completely in this equation: $\frac{1}{2}mv_0^2=\frac{1}{2}mv_1^2+mg\cdot 2r$
I understand canceling the first terms where m is multiplied my half, but I dont understand how the whole m can also get cancelled out so that the final result is: $\frac{1}{2}v_0^2=\frac{1}{2}v_1+g\cdot 2r$
It's because you can factor out the $m$ from the right side of the equation:
$$\frac{1}{2}mv_0^2=m\left(\frac{1}{2}v_1^2+2gr\right)$$
Now, when both sides are divided by $m$, they cancel.