To solve this equation, we will first simplify both sides of the equation.

On the left side, we can use the distributive property to expand the expression:

(3x - 4)(x - 2) = 3x(x - 9) - 3

3x(x - 2) - 4(x - 2) = 3x(x - 9) - 3

Now, we can simplify each side of the equation separately.

On the left side:

3x(x - 2) - 4(x - 2) = 3x^2 - 6x - 4x + 8

= 3x^2 - 10x + 8

On the right side:

3x(x - 9) - 3 = 3x^2 - 27x - 3

Now, we have the equation:

3x^2 - 10x + 8 = 3x^2 - 27x - 3

To solve for x, we can subtract 3x^2 from both sides of the equation:

-10x + 8 = -27x - 3

Next, we can add 27x to both sides of the equation:

17x + 8 = -3

Finally, we can subtract 8 from both sides of the equation:

17x = -11

Dividing both sides of the equation by 17, we find:

x = -11/17

Therefore, the solution to the equation is x = -11/17.