Solve each of the following equation and also verify your solution:
Question:

Solve each of the following equation and also verify your solution:
(x + 2)(x + 3) + (x − 3)(x − 2) − 2x(x + 1) = 0

Solution:

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

or $\mathrm{x}^{2}+5 \mathrm{x}+6+\mathrm{x}^{2}-5 \mathrm{x}+6-2 \mathrm{x}^{2}-2 \mathrm{x}=0$

or $12-2 \mathrm{x}=0$

or $\mathrm{x}=\frac{12}{2}=6$

Verification :

L. H. S. $=(6+2)(6+3)+(6-3)(6-2)-2 \times 6(6+1)$

$=72+12-84=0=\mathrm{R} .$ H. S.