a) (x-4)(x+3)-x^2+16=0

<=> x^2 + 3x-4x-12-x^2+16=0

<=>x^2-x-12-x^2+16=0

<=>  -x + 4 = 0

<=> -x = -4

<=>  x = 4

b) ( x^2 - 1 ) - 2x + 2 = 0

<=> (x - 1)^2 - 2x + 2 = 0

<=> ( x^2 - 2.x.1 + 1) - 2x + 2 = 0

<=> x^2 - 2x + 1 - 2x + 2 = 0

<=> x^2 - 4x + 3 = 0

<=> x^2 - x - 3x + 1 = 0

<=> x(x - 1) - 3(x - 1) = 0 

<=> ( x - 3 ) ( x - 1 ) = 0

TH1: x - 3 = 0

<=> x = 3

TH2: x - 1 = 0

<=> x = 1