Question
Solve the following equation and also verify your solution: $(x + 2)(x + 3) + (x − 3)(x − 2) − 2x(x + 1) = 0$
✓
Answer
$(x + 2)(x + 3) + (x - 3)(x - 2) - 2x(x + 1) = 0$
or $x^2 + 5x + 6 + x^2 - 5x + 6 - 2 x^2 - 2x = 0$
or $12 - 2x = 0$
or $x = \frac{12}{2} = 6$
Verification:
$\text{ L . H . S . }= (6 + 2)(6 + 3) + (6 - 3)(6 - 2) - 2 \times 6(6 + 1)$
$ = 72 + 12 - 84 = 0 =\text{ R . H . S .}$
or $x^2 + 5x + 6 + x^2 - 5x + 6 - 2 x^2 - 2x = 0$
or $12 - 2x = 0$
or $x = \frac{12}{2} = 6$
Verification:
$\text{ L . H . S . }= (6 + 2)(6 + 3) + (6 - 3)(6 - 2) - 2 \times 6(6 + 1)$
$ = 72 + 12 - 84 = 0 =\text{ R . H . S .}$
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