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

To simplify the expression 3x(x-2)-5x(x+3), we need to apply the distributive property and combine like terms.

Let's start by distributing the coefficients to the terms inside the parentheses:

3x(x-2) = 3x^2 - 6x -5x(x+3) = -5x^2 - 15x

Now we can combine the like terms:

(3x^2 - 6x) - (5x^2 + 15x)

To subtract the second expression, we need to distribute the negative sign to each term inside the parentheses:

3x^2 - 6x - 5x^2 - 15x

Now we can combine the like terms:

(3x^2 - 5x^2) + (-6x - 15x)

This simplifies to:

-2x^2 - 21x

So, the simplified expression is -2x^2 - 21x.