Solve the following equation and also verify your solution:

$\left(\mathrm{x}+2\right)\left(\mathrm{x}+3\right)+\left(\mathrm{x}-3\right)\left(\mathrm{x}-2\right)-2\mathrm{x}\left(\mathrm{x}+1\right)=0$

Solve the following equation and also verify your solution:

$\frac{\mathrm{x}}{2}-\frac{4}{5}+\frac{\mathrm{x}}{5}+\frac{3\mathrm{x}}{10}=\frac{1}{5}$

Solve the following equation and also verify your solution:

$\frac{7}{\mathrm{x}}+35=\frac{1}{10}$

Solve the following equation and also verify your solution:

$\frac{2\mathrm{x}-1}{3}-\frac{6\mathrm{x}-2}{5}=\frac{1}{3}$

Solve the following equation and also verify your solution:

$13\left(\mathrm{y}-4\right)-3\left(\mathrm{y}-9\right)-5\left(\mathrm{y}+4\right)=0$

Solve the following equation and also verify your solution:

$\frac{2}{3}\left(\mathrm{x}-5\right)-\frac{1}{4}\left(\mathrm{x}-2\right)=\frac{9}{2}$

Solve the following equation and also check your result in each case:

$\frac{2x+5}{3}=3x-10$

Solve the following equation and also check your result: $\frac{\mathrm{a}-8}{3}=\frac{\mathrm{a}-3}{2}$

Solve the following equation and also check your result in each case:

$\frac{7\mathrm{y}+2}{5}=\frac{6\mathrm{y}-5}{11}$