Simplify: (3x − 2)(2x − 3) + (5x − 3)(x + 1)

To simplify, we will proceed as follows:

(3x − 2)(2x − 3) + (5x − 3)(x + 1)

$=[(3 x-2)(2 x-3)]+[(5 x-3)(x+1)]$

$=[3 x(2 x-3)-2(2 x-3)]+[5 x(x+1)-3(x+1)] \quad$ (Distributive law)

$=6 x^{2}-9 x-4 x+6+5 x^{2}+5 x-3 x-3$

$=6 x^{2}+5 x^{2}-9 x-4 x+5 x-3 x-3+6 \quad$ (Rearranging)

$=11 x^{2}-11 x+3 \quad$ (Combining like terms)

Thus, the answer is $11 x^{2}-11 x+3$.