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

To simplify the expression 3x(x-2)-5x(x+3), we'll expand the brackets and combine like terms.

Expanding the first bracket: 3x(x-2) = 3x * x + 3x * (-2) = 3x^2 - 6x

Expanding the second bracket: -5x(x+3) = -5x * x - 5x * 3 = -5x^2 - 15x

Now, we can simplify the expression by combining like terms:

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

To subtract the second bracket, we need to distribute the negative sign to each term within the bracket:

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

Combining like terms:

(3x^2 - 5x^2) + (-6x - 15x) = -2x^2 - 21x

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