Solve for x by factoring x^2-4x+3=0

Thank you for any amount of help you can provide =)

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

ans: x = 3 and x = 1

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

x = 1 or x = 3