Hey, I'm sorry if this is in the wrong place, I wasn't too sure where to put a transformation question. No idea what I'm doing wrong, thanks for taking the time to look over my problem!

The question I've got here;

$\displaystyle

y=x^3-4x^2+x+6$ is stretched horizontally by a factor of 2 about the line x = 4 What is the resulting equation?

I started by moving the graph to the left by 4 units to line up x=4 with the y-axis. Which is what a reference problem in my textbook is doing,

$\displaystyle

y = (x+4)^3-4(x+4)^2+(x+4)+6

$

$\displaystyle y = (x+4)^3-4(x+4)^2+x+10

$

From here I stretched by a factor of 2 by replacing all $\displaystyle x$ with $\displaystyle \frac{1}{2}x$

$\displaystyle

y=(\frac{1}{2}x+4)^3-4(\frac{1}{2}x+4)^2+\frac{1}{2}x +10

$

$\displaystyle

y=(\frac{1}{2}x+4)^3-2(x+4)^2+\frac{1}{2}x +10

$

Lastly, I moved the graph back by 4 units to the right, to place it back with the line about which it was being stretched.

$\displaystyle

y=\frac{1}{2}x^3-2x^2+\frac{1}{2}x+6

$

I must be doing something wrong, as I don't see why the intermediate steps of translating it 4 units left and then back had anything to do with it.

The correct answer to this problem is

$\displaystyle

y=\frac{1}{8}x^3+\frac{1}{2}x^2-\frac{3}{2}x

$

I have NO idea how they could manage to get this! Does anyone have any idea how I'm going wrong? Thanks in advance for any and all help!