Solve the given equation for x, as shown below
[tex]\begin{gathered} 3(4x-6)^2-21=-9 \\ \Rightarrow3(4x-6)^2=-9+21=12 \\ \Rightarrow(4x-6)^2=\frac{12}{3}=4 \\ \Rightarrow(4x-6)=\pm\sqrt{4}=\pm2 \\ \Rightarrow4x=6\pm2 \\ \Rightarrow x=\frac{6\pm2}{4} \\ \Rightarrow x=1,2 \end{gathered}[/tex]