Let's solve each of the equations step by step.

### c) \((x + 4)^2 + (x + 6)^2 + 2(1 - x)(1 + x) = 0\)

1. Expand the terms:
\[
(x + 4)^2 = x^2 + 8x + 16
\]
\[
(x + 6)^2 = x^2 + 12x + 36
\]
\[
2(1 - x)(1 + x) = 2(1 - x^2) = 2 - 2x^2
\]

2. Combine everything:
\[
(x^2 + 8x + 16) + (x^2 + 12x + 36) + (2 - 2x^2) = 0
\]
This simplifies to:
\[
2x^2 + 20x + 54 - 2x^2 = 0 \implies 20x + 54 = 0
\]

3. Solve for \(x\):
\[
20x = -54 \implies x = -\frac{54}{20} = -\frac{27}{10} = -2.7
\]

### d) \((3 - 5x)(3 + 5x) + (5x + 1)^2 = 7\)

1. Use the difference of squares for \((3 - 5x)(3 + 5x)\):
\[
3^2 - (5x)^2 = 9 - 25x^2
\]

2. Expand \((5x + 1)^2\):
\[
(5x + 1)^2 = 25x^2 + 10x + 1
\]

3. Combine everything:
\[
9 - 25x^2 + 25x^2 + 10x + 1 = 7
\]
This simplifies to:
\[
10x + 10 = 7 \implies 10x = -3 \implies x = -\frac{3}{10} = -0.3
\]

### e) \(x^2 - 12x + 48 = 0\)

1. Use the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{12 \pm \sqrt{(-12)^2 - 4 \cdot 1 \cdot 48}}{2 \cdot 1} = \frac{12 \pm \sqrt{144 - 192}}{2}
\]
\[
= \frac{12 \pm \sqrt{-48}}{2} = \frac{12 \pm 4i\sqrt{3}}{2} = 6 \pm 2i\sqrt{3}
\]
The solutions are:
\[
x = 6 + 2i\sqrt{3}, \quad x = 6 - 2i\sqrt{3}
\]

### g) \(x^2 + 5x + 4 = 0\)

1. Factor the quadratic:
\[
(x + 1)(x + 4) = 0
\]

2. Set each factor to zero:
\[
x + 1 = 0 \implies x = -1
\]
\[
x + 4 = 0 \implies x = -4
\]

### h) \(4x^2 + 5x + 1 = 0\)

1. Use the quadratic formula:
\[
x = \frac{-5 \pm \sqrt{5^2 - 4 \cdot 4 \cdot 1}}{2 \cdot 4} = \frac{-5 \pm \sqrt{25 - 16}}{8}
\]
\[
= \frac{-5 \pm 3}{8}
\]

2. Calculate the solutions:
\[
x = \frac{-2}{8} = -\frac{1}{4}, \quad x = \frac{-8}{8} = -1
\]

### Summary of solutions:
- c) \(x = -2.7\)
- d) \(x = -0.3\)
- e) \(x = 6 + 2i\sqrt{3}, 6 - 2i\sqrt{3}\)
- g) \(x = -1, -4\)
- h) \(x = -\frac{1}{4}, -1\)