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

To simplify the expression 3x(x-2)-5x(x+3), we can 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 like terms by adding or subtracting the terms with the same exponent:

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

To combine like terms, we group the x^2 terms together and the x terms together:

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

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