Rearranging the equation f(x)=0 into the form x=g(x)

I think that he is asking what the purpose is NOT how to rearrange the another form.

It is used to find the solution of f(x) = 0.

Find the value for the initial x[0] so that f(x) is quite close to 0 by trial and error.

If you transfer it to x = g(x),

x[1] = g(x[0])
x[2] = g(x[1])
x[3] = g(x[2])
...
x[n+1] = g(x[n])
and so on... until you find that it is enough accuracy.

The simple way to do:
f(x) = 0
0= f(x)
x+0=x+ f(x)
x=x+f(x)=g(x)
or
0= f(x)
1+0= 1+f(x)
1=1+f(x)
x=x+xf(x)=g(x)

So, you see that there are a lot of ways to make x=g(x).