To solve the equation 3x(x-2)-x+2=0, we can start by simplifying the left side of the equation:

3x(x-2)-x+2 = 0
3x^2 - 6x - x + 2 = 0
3x^2 - 7x + 2 = 0

Now, we can try factoring the quadratic equation. However, since the coefficient of x^2 is not 1, factoring may not be possible. In this case, we can use the quadratic formula to find the solutions.

The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 3, b = -7, and c = 2. Plugging these values into the quadratic formula, we get:

x = (-(-7) ± √((-7)^2 - 4(3)(2))) / (2(3))
x = (7 ± √(49 - 24)) / 6
x = (7 ± √25) / 6
x = (7 ± 5) / 6

This gives us two possible solutions:

x = (7 + 5) / 6 = 12 / 6 = 2
x = (7 - 5) / 6 = 2 / 6 = 1/3

Therefore, the solutions to the equation 3x(x-2)-x+2=0 are x = 2 and x = 1/3.