To solve the equation X² - (1.2x - 3)(3 + 1.2x) = 0.2x(1.5 - 2.2x²), we need to simplify both sides of the equation and solve for x.

Expanding the left side:
X² - (1.2x - 3)(3 + 1.2x)
= X² - (3 + 1.2x)(3) + (3 + 1.2x)
= X² - 9 - 3.6x + 3 + 1.2x
= X² - 6.4x - 6

Expanding the right side:
0.2x(1.5 - 2.2x²)
= 0.2x + 0.44x³

Now our equation becomes:
X² - 6.4x - 6 = 0.2x + 0.44x³

Rearranging the equation:
x³ + 5.76x + 6 = 0

Unfortunately, this cubic equation doesn't have a simple solution like linear or quadratic equations. You may need to use numerical methods to find the solution.