By over C I mean it has a solution that is a complex number

My Attempt:

4z^2-4z+17=(4z^2-4z+4)-4+17

................=(2z-2)^2 +13

................=(2z-2)^2 - (Squareroot of (13)*i)^2

................=((2z+2)+(Squareroot of 13 *i))((2z+2)-(Squareroot of 13 *i))

However, the real answer is (2z-1+4i)(2z-1-4i)

I can factorise questions such as z^2-4z+17 but when there is a number infront of z^2 I do not know how to do it.

Thank you for any help .