Ответ:

  1. \(4x^3y-6x^2y^3=\boxed{2x^2y(2x-3y^2)}\).
  2. \(5a^3-15a^2b+20ab^2=\boxed{5a(a^2-3ab+4b^2)}\).
  3. \(6mn^2-9n^4+12m^2n^3=\boxed{3n^2(2m-3n^2+4m^2n)}\).
  4. \(-3xy^2-15x^2y-21x^2y^2=\boxed{-3xy(y+5x+7xy)}\).
  5. \(12a^2b-18ab^2-30ab^3=\boxed{6ab(2a-3b-5b^2)}\).
  6. \(-6ax^2+9x^2-12x^4-30x^2=\boxed{-3x^2(2a+4x^2+7)}\).