1)
\(\frac{3x-2}{6}-\frac{4-3x}{18}=\frac{4-x}{9}\\ \Leftrightarrow\frac{9x-6}{18}-\frac{4-3x}{18}-\frac{8-2x}{18}=0\\ \Leftrightarrow\frac{9x-6-4+3x-8+2x}{18}=0\\ \Leftrightarrow\frac{14x-18}{18}=0\\ \Rightarrow14x-18=0\\ \Rightarrow x=\frac{18}{14}=\frac{6}{7}\)
2)
\(\frac{2+3x}{6}-x+2=\frac{x-7}{9}\\ \Leftrightarrow\frac{6+9x}{18}-\frac{18x-36}{18}-\frac{2x-14}{18}=0\\ \Leftrightarrow\frac{6+9x-18x+36-2x+14}{18}=0\\ \Leftrightarrow\frac{56-11x}{18}=0\\ \Rightarrow56-11x=0\\ \Rightarrow x=\frac{56}{11}\)
3)
\(2x\cdot\left(x-5\right)+3x\cdot\left(x-5\right)=0\\ \Leftrightarrow\left(2x+3x\right)\cdot\left(x-5\right)=0\\ \Leftrightarrow5x\cdot\left(x-5\right)=0\\ \Rightarrow\left[{}\begin{matrix}5x=0\\x-5=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=0\\x=5\end{matrix}\right.\)
