Simplify the expression $2x(x^2-2x-3)-x^2(3x-5)$.

1. Problem Description

Simplify the expression $2x(x^2-2x-3)-x^2(3x-5)$.

2. Solution Steps

First, distribute $2x$ to the terms inside the first parenthesis:

$2x(x^2 - 2x - 3) = 2x^3 - 4x^2 - 6x$

Next, distribute $-x^2$ to the terms inside the second parenthesis:

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

Now, combine the two resulting expressions:

$(2x^3 - 4x^2 - 6x) + (-3x^3 + 5x^2) = 2x^3 - 4x^2 - 6x - 3x^3 + 5x^2$

Combine like terms:

$2x^3 - 3x^3 - 4x^2 + 5x^2 - 6x = (2-3)x^3 + (-4+5)x^2 - 6x$

$= -x^3 + x^2 - 6x$

3. Final Answer

$-x^3 + x^2 - 6x$