(x-1)^2 = (x+3)^2

(x-1)(x-1) = (x+3)(x+3)

x^2 - 2x + 1 = x^2 + 6x + 9

Subtract x^2 from both sides:

-2x + 1 = 6x + 9

Add 2x to both sides:

1 = 8x + 9

Subtract 9 from both sides:

-8 = 8x

Divide by 8:

x = -1

Therefore, the solution to the equation (x-1)^2 = (x+3)^2 is x = -1.