Let's simplify the left side first:

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

Now expand the right side:

(x - 3)^2 - 10
= (x - 3)(x - 3) - 10
= x^2 - 3x - 3x + 9 - 10
= x^2 - 6x - 1

So the equation becomes:

x^2 + x - 1 = x^2 - 6x - 1

Since the x^2 terms cancel out, x - 1 = -6x

Now let's solve for x:

x - 1 = -6x
7x = 1
x = 1/7

So the solution to the equation is x = 1/7.