Any advise much appreciated

I have the following equation;

x^2 - 4x - 3 = 0

I tried the quadratic formula but could not get any answers to = 0

So I tried to solve the equation by factorisation. Here are some attempts that I have tried, where I don't want to believe that the equation cannot be factored, rather I think I may just be missing something?

x^2 - 4x - 3 = 0

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

(x - 1)(x + 3) = x^2 + 3x - x - 4

(x + 4)(x - 1) = x^2 -x + 4x - 4

(x - 1)(x + 4) = x^2 +4x - x - 4

(x + 7)(x - 4) = x^2 -4x + 7x - 28

(x + 2)(x - 2) = x^2 -2x + 2x -4 = x^2 - 4x -4

My problem is that I can't re-generate the -3

David

(x + 3)(x - 1) = x^2 -x + 3x - 3 = x^2 - 4x - 3 = 0

Sorry