$$7 \cdot (2x - 1) + 5 \cdot (3x + 2) = 32$$
$$14x - 7 + 15x + 10 = 32$$
$$29x + 3 = 32$$
$$29x = 32 - 3$$
$$29x = 29$$
$$x = \frac{29}{29}$$
$$x = 1$$