To solve this equation, we will first expand the expression on the left side of the equation:

(x-1)(x+1) - (x-1)

Expanding the first term using the distributive property:

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

Simplify by combining like terms:

= x^2 - 1

Now set the expression equal to 0 and solve for x:

x^2 - 1 = 0

Add 1 to both sides:

x^2 = 1

Take the square root of both sides:

x = ±1

The solutions to the equation are x = 1 and x = -1.