First, simplify the expression:
[tex]\begin{gathered} 3\lbrack2x-(3x-4)\rbrack-6(x-3) \\ =3\lbrack2x-3x+4-6(x-3) \\ =3(2x)+3(-3x)+3(4)-6(x-3) \\ =6x-9x+12-6x+18 \\ =6x-9x-6x+12+18 \\ =-3x-6x+12+18 \\ =-9x+12+18 \\ =-9x+30 \end{gathered}[/tex]Then:
[tex]3\lbrack2x-(3x-4)\rbrack-6(x-3)=-9x+30^{}[/tex]To find the zero of the given expression, find the zero of -9x+30:
[tex]\begin{gathered} -9x+30=0 \\ \Rightarrow-9x=-30 \\ \Rightarrow x=\frac{-30}{-9} \\ \therefore x=\frac{10}{3} \end{gathered}[/tex]Therefore, the zero of the given expression is 10/3.
