$$2x(x-3)+5(x-3)$$
$\left(x-3\right)\left(2x+5\right)$
$$2x^{2}-6x+5\left(x-3\right)$$
$$2x^{2}-6x+5x-15$$
$$2x^{2}-x-15$$
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$2x^{2}-x-15$