It looks like you're trying to work with a mathematical equation, but the formatting appears a bit jumbled. Let's clarify the equation you've written:

You seem to have the equation:

\[
x^2 + y^2 + 4y + 13 = 6x
\]

To analyze this equation, let's rearrange it into a standard form. We'll move all terms to one side:

\[
x^2 - 6x + y^2 + 4y + 13 = 0
\]

Now, let's complete the square for both the \(x\) and \(y\) terms.

### Completing the square for \(x\):

1. For \(x^2 - 6x\):

\[
x^2 - 6x = (x - 3)^2 - 9
\]

### Completing the square for \(y\):

2. For \(y^2 + 4y\):

\[
y^2 + 4y = (y + 2)^2 - 4
\]

### Substitute these back into the equation:

Now we substitute these completed squares into the equation:

\[
(x - 3)^2 - 9 + (y + 2)^2 - 4 + 13 = 0
\]

Simplifying this:

\[
(x - 3)^2 + (y + 2)^2 - 9 - 4 + 13 = 0
\]

\[
(x - 3)^2 + (y + 2)^2 + 0 = 0
\]

This simplifies to:

\[
(x - 3)^2 + (y + 2)^2 = 0
\]

### Conclusion:

The equation \((x - 3)^2 + (y + 2)^2 = 0\) implies that both squares must equal zero. Thus:

\[
x - 3 = 0 \quad \Rightarrow \quad x = 3
\]

\[
y + 2 = 0 \quad \Rightarrow \quad y = -2
\]

The solution to the original equation is the single point:

\[
(x, y) = (3, -2)
\]

If you need further assistance or a different approach, feel free to ask!