First move all terms to one side:
[tex]m^2=2m\implies m^2-2m=0[/tex]
Then all terms on the left side share a common factor of [tex]m[/tex]:
[tex]m(m-2)=0[/tex]
The zero product product property says that if [tex]ab=0[/tex], then [tex]a=0[/tex] or [tex]b=0[/tex]. So either [tex]m=0[/tex] or [tex]m-2=0\implies m=2[/tex].