The problem asks to simplify the expression $(2x - 3)(3x^2 - 2x + 5)$.

1. Problem Description

The problem asks to simplify the expression $(2x - 3)(3x^2 - 2x + 5)$.

2. Solution Steps

To simplify the expression, we need to multiply the two polynomials. We can use the distributive property (also known as the FOIL method for binomials).

$(2x - 3)(3x^2 - 2x + 5) = 2x(3x^2 - 2x + 5) - 3(3x^2 - 2x + 5)$

Now, we distribute $2x$ and $-3$ to each term in the second polynomial:

$2x(3x^2) + 2x(-2x) + 2x(5) - 3(3x^2) - 3(-2x) - 3(5)$

Multiplying each term:

$6x^3 - 4x^2 + 10x - 9x^2 + 6x - 15$

Now, combine like terms:

$6x^3 + (-4x^2 - 9x^2) + (10x + 6x) - 15$

$6x^3 - 13x^2 + 16x - 15$

3. Final Answer

The simplified expression is $6x^3 - 13x^2 + 16x - 15$.