$\frac{ 2x+7 }{ 3 }-\frac{ x-3 }{ 2 }-4x=0$
Multiply both sides of the equation by $6$$2\left( 2x+7 \right)-3\left( x-3 \right)-24x=0$
Distribute $2$ through the parentheses$4x+14-3\left( x-3 \right)-24x=0$
Distribute $-3$ through the parentheses$4x+14-3x+9-24x=0$
Collect like terms$-23x+14+9=0$
Add the numbers$-23x+23=0$
Move the constant to the right-hand side and change its sign$-23x=-23$
Divide both sides of the equation by $-23$$x=1$