a) To solve this equation, we can start by expanding the expression inside the parentheses:

4x^2 - 25 - (2x - 5)(2x + 7) = 0
4x^2 - 25 - (4x^2 - 3x - 35) = 0
4x^2 - 25 - 4x^2 + 3x + 35 = 0
3x + 10 = 0

Now, we can solve for x:

3x = -10
x = -10/3

b) To solve this equation, we can start by expanding the expression inside the parentheses:

x^3 + 27 + (x + 3)(x - 9) = 0
x^3 + 27 + (x^2 - 9x + 3x - 27) = 0
x^3 + 27 + x^2 - 6x = 0
x^3 + x^2 - 6x + 27 = 0

Unfortunately, this equation does not have a simple solution. It can be solved using numerical methods or factoring techniques.

c) To solve this equation, we can try factoring by grouping:

2x^3 + 3x^2 + 2x + 3 = 0
(x^2 + 1)(2x + 3) = 0

Now, we can set each factor equal to zero:

x^2 + 1 = 0
x^2 = -1
x = ±√(-1)
x = ±i

2x + 3 = 0
2x = -3
x = -3/2

So the solutions to the equation are x = -3/2 and x = ±i.

d) To solve this equation, we can start by factoring out the common factor of (x + 7):

x^2(x + 7) - 4(x + 7) = 0
(x + 7)(x^2 - 4) = 0

Now, we can set each factor equal to zero:

x + 7 = 0
x = -7

x^2 - 4 = 0
(x + 2)(x - 2) = 0

Now, we can set each factor equal to zero:

x + 2 = 0
x = -2

x - 2 = 0
x = 2

So the solutions to the equation are x = -7, x = -2, and x = 2.