(x-2)^2 (x-3) = 12 (x-2)

Expanding the left side:

(x^2 - 4x + 4) * (x-3) = 12x - 24

Multiplying the terms inside the parentheses:

x^3 - 3x^2 - 4x^2 + 12x + 4x - 12 = 12x - 24

Combining like terms:

x^3 - 7x^2 + 16x - 12 = 12x - 24

Rearranging the terms:

x^3 - 7x^2 + 16x - 12 - 12x + 24 = 0

x^3 - 7x^2 + 4x + 12 = 0

Therefore, the solution to the equation is x^3 - 7x^2 + 4x + 12 = 0.