This equation can be simplified by using the properties of logarithms.

First, let's rewrite the equation using a different notation. Let lg(x) represent log base 10 of x.

So, the given equation becomes:

lg^2(x + 1) = lg(x + 1)lg(x - 1) + 2lg^2(x - 1)

Now, we can simplify this equation using the following properties of logarithms:

Applying these properties, we get:

lg(x + 1)^2 = lg((x + 1)(x - 1)) + lg((x - 1)^2)

Expanding the terms in the equation:

lg((x + 1)^2) = lg(x^2 - 1) + lg(x^2 - 2x + 1)

Now, we can simplify further and solve for x.