Solve equations using factorization method:
$(x + 3)^{2} - 4 (x + 3) - 5 = 0$

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Solution

Step : Factorising the equation:
$(x + 3)^{2} - 4 (x + 3) - 5 = 0$

Let $x + 3 = y$
$\Rightarrow y^{2} - 4 y - 5 = 0$
$\Rightarrow y^{2} - 5 y + y - 5 = 0$ {factorizing left hand side}
$\Rightarrow y (y - 5) + 1 (y - 5) = 0$
$\Rightarrow (y - 5) (y + 1) = 0$
$\Rightarrow y - 5 = 0 o r y + 1 = 0$
{Zero product rule}
$\Rightarrow y = 5 o r y = - 1$
As $y = x + 3$
$\Rightarrow x + 3 = 5 o r x + 3 = - 1$
$\Rightarrow x = 2 o r x = - 4$
Hence, the required answer is $x = 2 o r x = - 4$

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