Let's first expand the expression on the left side of the equation:

(x-4)(x² + 15x + 50)(x-2) = 18x²

Expanding the expression, we get:

(x³ + 15x² + 50x - 4x² - 60x - 200)(x-2) = 18x²

Now, simplify the terms:

x³ + 15x² + 50x - 4x² - 60x - 200 = 18x²

Combine like terms:

x³ + 11x² - 10x - 200 = 18x²

Rearrange the terms to set it equal to zero:

x³ + 11x² - 10x - 200 - 18x² = 0

Combine like terms:

x³ - 7x² - 10x - 200 = 0

Therefore, the solution to the given equation is x³ - 7x² - 10x - 200 = 0.