$$x(x+2)+3(x+2)$$
$\left(x+2\right)\left(x+3\right)$
$$x^{2}+2x+3\left(x+2\right)$$
$$x^{2}+2x+3x+6$$
$$x^{2}+5x+6$$
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$x^{2}+5x+6$