\(1.\\ \left(3x+2\right)\left(2-3x\right)=25x^2-\left(4x+3\right)^2\\ 6x-9x^2+4-6x=25x^2-16x^2-24x-9\\ 4-9x^2=9x^2-24x-9\\ 18x^2-24x-13=0\\ x^2-\dfrac{4}{3}x-\dfrac{13}{18}=0\\ x^2-2.\dfrac{2}{3}x+\dfrac{4}{9}=\dfrac{13}{18}+\dfrac{4}{9}=\dfrac{7}{6}\\ \left(x-\dfrac{2}{3}\right)^2=\dfrac{7}{6}\\ \Rightarrow\left[{}\begin{matrix}x-\dfrac{2}{3}=\sqrt{\dfrac{7}{6}}\\x-\dfrac{2}{3}=-\sqrt{\dfrac{7}{6}}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\sqrt{\dfrac{7}{6}}+\dfrac{2}{3}\\x=\dfrac{2}{3}-\sqrt{\dfrac{7}{6}}\end{matrix}\right.\)
\(2.\\ \left(\dfrac{x-2}{3}\right)^2+\left(\dfrac{x-3}{2}\right)^2-\dfrac{\left(x-2\right)\left(x-3\right)}{3}=4\\ \dfrac{x^2-4x+4}{9}+\dfrac{x^2-6x+9}{4}-\dfrac{x^2-5x+6}{3}=0\\ \dfrac{4x^2-16x+16}{36}+\dfrac{9x^2-54x+81}{36}-\dfrac{12x^2-60x+72}{36}=\dfrac{144}{36}\\ \Rightarrow4x^2-16x+16+9x^2-54x+81-12x^2+60x-72-144=0\\ x^2-10x-119=0\\ x^2-2.5.x+25-144=0\\ \left(x-5\right)^2=144\\ \Rightarrow\left[{}\begin{matrix}x-5=12\\x-5=-12\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=17\\x=-7\end{matrix}\right.\)
