The equation is given as,
[tex]2(x-3)+3=6x-5[/tex]According to the distributive property,
[tex]a\cdot(b-c)=(a\cdot b)-(a\cdot c)[/tex]Applying the property and resolving the parenthesis,
[tex]\begin{gathered} 2(x)-2(3)+3=6x-5 \\ 2x-6+3=6x-5 \\ 2x-3=6x-5 \end{gathered}[/tex]Subtract 2x on both sides,
[tex]\begin{gathered} 2x-3-2x=6x-5-2x \\ -3+0=4x-5 \\ 4x-5=-3 \end{gathered}[/tex]Add 5 on both sides,
[tex]\begin{gathered} 4x-5+5=-3+5 \\ 4x+0=2 \\ 4x=2 \end{gathered}[/tex]Divide both sides by 4,
[tex]\begin{gathered} \frac{4x}{4}=\frac{2}{4} \\ x=\frac{1}{2} \end{gathered}[/tex]Thus, the solution of the given equation is,
[tex]x=\frac{1}{2}[/tex]