Bugged LaTeX

\left[\begin{array}{l}\left\{\begin{array}{l}2-3x<0\\ -9{x}^{2}+9x+4\ge 0\end{array}\right.\\ \left\{\begin{array}{l}2-3x\ge 0\\ -9{x}^{2}+9x+4>{\left(2-3x\right)}^{2}\end{array}\right.\end{array}\right.\Rightarrow \left[\begin{array}{l}\left\{\begin{array}{l}\frac{2}{3}<x\\ -9\left(x+\frac{1}{3}\right)\left(x-\frac{1}{4}\right)\ge 0\end{array}\right.\\ \left\{\begin{array}{l}\frac{2}{3}\ge x\\ -9{x}^{2}+9x+4>4-6x+9x^2\end{array}\right.\end{array}\right.\Rightarrow \left[\begin{array}{l}\left\{\begin{array}{l}\frac{2}{3}<x\\ x\in \left[-\frac{1}{3};\frac{4}{3}\right]\end{array}\right.\\ \left\{\begin{array}{l}\frac{2}{3}\ge x\\ 0>18{x}^{2}-21x\end{array}\right.\end{array}\right.\Rightarrow \left[\begin{array}{c}x\in \left(\frac{2}{3};\frac{4}{3}\right]\\ \left\{\begin{array}{l}\frac{2}{3}\ge x\\ x\in \left(0;\frac{7}{6}\right)\end{array}\right.\end{array}\right.