To solve
[tex]3(2x+y)=5y+3,[/tex]for y. First, we apply the distributive property on the left of the equation:
[tex]3\cdot2x+3y=5y+3.[/tex]Simplifying we get:
[tex]6x+3y=5y+3.[/tex]Now, we subtract 6x from the above equation:
[tex]6x+3y-6x=5y+3-6x\text{.}[/tex]Simplifying we get:
[tex]3y=5y-6x+3.[/tex]Subtracting 5y, we get:
[tex]\begin{gathered} 3y-5y=5y-6x+3-5y, \\ -2y=-6x+3. \end{gathered}[/tex]Finally, dividing by -2, we get:
[tex]y=\frac{-6x+3}{-2}=\frac{6x-3}{2}\text{.}[/tex]Answer:
[tex]y=\frac{6x-3}{2}\text{.}[/tex]