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I've opened the image. I'll now work through the exercises shown in the document.

### Übung 5: Vervollständigen Sie den Lösungsweg (Complete the solution process)

The equation provided is:

\[
4x(2x - 9) - 10x = (x - 7)(8x - 4) - 2(x + 4)
\]

We will follow the steps given in the table to solve it:

1. Expand both sides:
   - Left-hand side:
   \[
   4x(2x - 9) = 8x^2 - 36x
   \]
   So, \( 8x^2 - 36x - 10x = 8x^2 - 46x \)
   - Right-hand side:
   \[
   (x - 7)(8x - 4) = 8x^2 - 56x - 4x + 28 = 8x^2 - 60x + 28
   \]
   Subtract \(2(x + 4)\):
   \[
   2(x + 4) = 2x + 8
   \]
   So, the right-hand side becomes:
   \[
   8x^2 - 60x + 28 - 2x - 8 = 8x^2 - 62x + 20
   \]

2. Simplify both sides:
   The equation now is:
   \[
   8x^2 - 46x = 8x^2 - 62x + 20
   \]

3. Subtract \(8x^2\) from both sides:
   \[
   -46x = -62x + 20
   \]

4. Add \(62x\) to both sides:
   \[
   62x - 46x = 20 \quad \Rightarrow \quad 16x = 20
   \]

5. Divide by 16:
   \[
   x = \frac{20}{16} = \frac{5}{4}
   \]

So, the solution to Übung 5 is \( x = \frac{5}{4} \).

---

### Übung 6: Ordnen Sie die richtige Lösung zu (Assign the correct solution)

In this exercise, we need to simplify each equation and match it with the appropriate answer. I'll expand each expression:

a) \( 2n^2 - (n + 12)(2n + 3) = 18 \)
   \[
   (n + 12)(2n + 3) = 2n^2 + 3n + 24n + 36 = 2n^2 + 27n + 36
   \]
   Therefore:
   \[
   2n^2 - (2n^2 + 27n + 36) = 18
   \]
   Simplifying:
   \[
   -27n - 36 = 18 \quad \Rightarrow \quad -27n = 54 \quad \Rightarrow \quad n = -2
   \]

b) \( 15n - (3n - 5)(4n + 5) = 5 - 12n^2 \)
   \[
   (3n - 5)(4n + 5) = 12n^2 + 15n - 20n - 25 = 12n^2 - 5n - 25
   \]
   So:
   \[
   15n - (12n^2 - 5n - 25) = 5 - 12n^2
   \]
   Simplifying:
   \[
   15n - 12n^2 + 5n + 25 = 5 - 12n^2 \quad \Rightarrow \quad 20n + 25 = 5
   \]
   Solving for \(n\):
   \[
   20n = -20 \quad \Rightarrow \quad n = -1
   \]

I'll continue solving the rest of the questions. Would you like to see the rest of the steps for Übung 6 and Übung 7?

Explore our detailed guide on solving complex algebraic equations involving distributive properties and quadratic solutions. This guide provides clear steps to understand and solve equations, making it suitable for high school students learning advanced algebra concepts.

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