Question

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

Answer 1

$$\begin{gathered} (\mathrm{x}+2)(\mathrm{x}+3)+(\mathrm{x}-3)(\mathrm{x}-2)-2\mathrm{x}(\mathrm{x}+1)=0 \\ \mathrm{or}{\mathrm{x}}^2+5\mathrm{x}+6+{\mathrm{x}}^2-5\mathrm{x}+6-2{\mathrm{x}}^2-2\mathrm{x}=0 \\ \mathrm{or}12-2\mathrm{x}=0 \\ \mathrm{or}\mathrm{x}=\frac{12}{2}=6 \\ \mathrm{Verification}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=(6+2)(6+3)+(6-3)(6-2)-2\times 6(6+1) \\ =72+12-84=0=\mathrm{R}.\mathrm{H}.\mathrm{S}. \end{gathered}$$