Solve for $x$ : $(5 x + 1) (x + 3) - 8$ $=$ $5 (x + 1) (x + 2)$ .

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Solution

Given, $(5 x + 1) (x + 3) - 8 = 5 (x + 1) (x + 2)$

$\Rightarrow$ $5 x^{2} + 15 x + x + 3 - 8 = 5 (x^{2} + 2 x + x + 2)$ ...[By Distribution Law]

$\Rightarrow$ $5 x^{2} + 16 x - 5 = 5 (x^{2} + 3 x + 2)$

$\Rightarrow$ $5 x^{2} + 16 x - 5 = 5 x^{2} + 15 x + 10$

$\Rightarrow$ $16 x - 5 = 15 x + 10$ ...[Cancelling $5 x^{2}$ on both sides].

Transposing $x$ terms to one side, we get,
$\Rightarrow$ $16 x - 15 x = 5 + 10$

$\Rightarrow$ $x = 15$ .

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