To solve the equations given, let's start with each one.

### For Equation c:
\[
(2x + 1)^2 - 9(x - 3)^2 = 0
\]

1. **Move \(9(x - 3)^2\) to the right side**:
\[
(2x + 1)^2 = 9(x - 3)^2
\]

2. **Take the square root of both sides**:
\[
2x + 1 = 3(x - 3) \quad \text{or} \quad 2x + 1 = -3(x - 3)
\]

3. **Solve the first equation**:
\[
2x + 1 = 3x - 9 \implies x = 10
\]

4. **Solve the second equation**:
\[
2x + 1 = -3x + 9 \implies 5x = 8 \implies x = \frac{8}{5}
\]

Thus, the solutions for equation c are:
\[
x = 10 \quad \text{and} \quad x = \frac{8}{5}
\]

### For Equation d:
\[
x^2 - 9 = (x - 3)(x + 5)
\]

1. **Expand the right side**:
\[
(x - 3)(x + 5) = x^2 + 5x - 3x - 15 = x^2 + 2x - 15
\]

2. **Set the equation**:
\[
x^2 - 9 = x^2 + 2x - 15
\]

3. **Subtract \(x^2\) from both sides**:
\[
-9 = 2x - 15
\]

4. **Solve for \(x\)**:
\[
2x = 6 \implies x = 3
\]

Thus, the solution for equation d is:
\[
x = 3
\]

### Summary of Solutions:
- For equation c: \(x = 10\) and \(x = \frac{8}{5}\)
- For equation d: \(x = 3\)