To solve the equation 3x(x+5)-2(x+5)=0, we can first simplify the expression on the left side of the equation:

3x(x+5)-2(x+5) = 3x^2 + 15x - 2x - 10

Next, we combine like terms:

3x^2 + 15x - 2x - 10 = 3x^2 + 13x - 10

Now, we set the expression equal to zero:

3x^2 + 13x - 10 = 0

To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, factoring is not straightforward, so we will use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 3, b = 13, and c = -10. Substituting these values into the quadratic formula:

x = (-13 ± √(13^2 - 4(3)(-10))) / (2(3))

Simplifying further:

x = (-13 ± √(169 + 120)) / 6
x = (-13 ± √289) / 6
x = (-13 ± 17) / 6

This gives us two possible solutions:

x = (-13 + 17) / 6 = 4/6 = 2/3
x = (-13 - 17) / 6 = -30/6 = -5

Therefore, the solutions to the equation 3x(x+5)-2(x+5)=0 are x = 2/3 and x = -5.