To solve these equations, we need to simplify and solve each one step by step. Here’s how you can approach them:

### 15)
\[
\sqrt{4x - 12} - \sqrt{9x - 27} + \frac{\sqrt{25x - 75}}{4} - 3 = 0
\]

1. Simplify the square roots:
\(\sqrt{4x - 12} = \sqrt{4(x - 3)} = 2\sqrt{x - 3}\)
\(\sqrt{9x - 27} = \sqrt{9(x - 3)} = 3\sqrt{x - 3}\)
\(\sqrt{25x - 75} = \sqrt{25(x - 3)} = 5\sqrt{x - 3}\)

2. Substitute back:
\(2\sqrt{x - 3} - 3\sqrt{x - 3} + \frac{5\sqrt{x - 3}}{4} - 3 = 0\)

3. Combine like terms:
\(-\sqrt{x - 3} + \frac{5\sqrt{x - 3}}{4} - 3 = 0\)

4. Convert into a single fraction:
\(-\frac{4}{4}\sqrt{x - 3} + \frac{5}{4}\sqrt{x - 3} = 3\)

5. Solve:
\(\frac{1}{4}\sqrt{x - 3} = 3\)
\(\sqrt{x - 3} = 12\)
\(x - 3 = 144\)
\(x = 147\)

### 16)
\[
\sqrt{16x - 48} - 8\sqrt{4x - 12} + \frac{2}{3}\sqrt{9x - 27} = -20
\]

1. Simplify the square roots:
\(\sqrt{16x - 48} = 4\sqrt{x - 3}\)
\(8\sqrt{4x - 12} = 8(2\sqrt{x - 3}) = 16\sqrt{x - 3}\)
\(\frac{2}{3}\sqrt{9x - 27} = \frac{2}{3}(3\sqrt{x - 3}) = 2\sqrt{x - 3}\)

2. Substitute back:
\(4\sqrt{x - 3} - 16\sqrt{x - 3} + 2\sqrt{x - 3} = -20\)

3. Combine like terms:
\(-10\sqrt{x - 3} = -20\)

4. Solve:
\(\sqrt{x - 3} = 2\)
\(x - 3 = 4\)
\(x = 7\)

### 17)
\[
\sqrt{9x - 9} - 3\sqrt{x - 1} + \frac{5}{2}\sqrt{16x - 16} = 30
\]

1. Simplify the square roots:
\(\sqrt{9x - 9} = 3\sqrt{x - 1}\)
\(\frac{5}{2}\sqrt{16x - 16} = \frac{5}{2}(4\sqrt{x - 1})=10\sqrt{x-1}\)

2. Substitute back:
\(3\sqrt{x - 1} - 3\sqrt{x - 1} + 10\sqrt{x - 1} = 30\)

3. Simplify:
\(10\sqrt{x - 1} = 30\)

4. Solve:
\(\sqrt{x - 1} = 3\)
\(x - 1 = 9\)
\(x = 10\)

### 18)
\[
\frac{3}{2}\sqrt{4 + 8x} - \frac{5}{3}\sqrt{9 + 18x} + \frac{1}{4}\sqrt{16 + 32x} = 1
\]

1. Simplify the square roots:
\(\sqrt{4 + 8x} = \sqrt{4(1 + 2x)} = 2\sqrt{1 + 2x}\)
\(\sqrt{9 + 18x} = \sqrt{9(1 + 2x)} = 3\sqrt{1 + 2x}\)
\(\sqrt{16 + 32x} = \sqrt{16(1 + 2x)} = 4\sqrt{1 + 2x}\)

2. Substitute back:
\(\frac{3}{2}(2\sqrt{1 + 2x}) - \frac{5}{3}(3\sqrt{1 + 2x}) + \frac{1}{4}(4\sqrt{1 + 2x}) = 1\)

3. Simplify:
\(3\sqrt{1 + 2x} - 5\sqrt{1 + 2x} + \sqrt{1 + 2x} = 1\)

4. Combine like terms:
\(-\sqrt{1 + 2x} = 1\)

5. Solve:
(This is not solvable due to negative square root, check for correct interpretation or re-evaluate conditions.)

Make sure to double-check calculations or constraints on variables to ensure accounting for domain restrictions or other mathematical properties.