To simplify this expression, we first need to expand the terms in the equation:

(-7x + 9y)^2 = (-7x + 9y)(-7x + 9y)
= 49x^2 - 63xy + 81y^2

Now, let's expand the second term:

-14x(4x - 9y) = -56x^2 + 126xy

Finally, let's expand the third term:

7x^2 = 7x^2

Putting it all together, we have:

(49x^2 - 63xy + 81y^2) - (56x^2 + 126xy) + 7x^2
= 49x^2 - 63xy + 81y^2 - 56x^2 - 126xy + 7x^2
= 0x^2 - 189xy + 81y^2
= -189xy + 81y^2

Therefore, the simplified expression is -189xy + 81y^2.