The expression you've provided seems to have formatting issues, but I'll interpret it as best as I can and simplify it. It appears to involve a logarithmic function and some constants or variables.

It looks like the expression is:

$1 = \left(2u^2 + 8au + 16a^2 \ln|u|\right) - 4a - a$

Let's simplify this step by step.

Step 1: Simplify the constants

Combine the constants on the right-hand side: $-4a - a = -5a$

So the equation becomes: $1 = 2u^2 + 8au + 16a^2 \ln|u| - 5a$

Step 2: Isolate the terms with $u$

To isolate the terms involving $u$, you can write the equation as: $2u^2 + 8au + 16a^2 \ln|u| = 1 + 5a$

This equation is simplified but does not have a straightforward solution for $u$ because of the logarithmic term. Depending on the context, you may need to solve this numerically or explore specific values for $a$.

Would you like further details or assistance with solving this for specific values of $u$ or $a$? Here are some related questions that could help expand on this:

1. How can we solve the quadratic equation without the logarithmic term?
2. What happens to the equation if we assume $u$ is very large or very small?
3. Can the equation be solved numerically for a given value of $a$?
4. What are the implications of the logarithmic term $\ln|u|$ in solving for $u$?
5. How does the equation change if we set $a = 0$?

Tip: When dealing with complex expressions involving logarithms, consider whether a numerical solution or approximation might be more practical than an algebraic one.