Hi..... Please, follow me, step by step...
[tex]\dfrac{2m}{5}+3=7(4m-3)\\
\dfrac{2m+5.3=5.7(4m-3)}{\not 5}\rightarrow 2m+5.3=5.7(4m-3)\rightarrow\\
2m+15=35(4m-3)\rightarrow 2m+15=140m-105\rightarrow\\
15+105=140m-2m\rightarrow 138m=120\rightarrow (2.3.23)m=2.2.2.3.5\rightarrow\\
m=\dfrac{\not 2.\not 3.\,23}{\not 2.\,2.\,2.\not 3.\,5}\rightarrow \boxed{m=\dfrac{23}{20}}[/tex]
Thank you for your trust... :)