Which Quadratic equation is equivalent to (x-4)^2-(x-4)-6=0

For this case, we must find the quadratic equation equivalent to: [tex](x-4) ^ 2- (x-4) -6 = 0[/tex]By definition we have to: [tex](a-b) ^ 2 = a^2-2ab + b ^ 2[/tex]So: [tex](x-4) ^ 2 = x ^ 2-2 (x) (4) + 4 ^ 2 = x ^ 2-8x + 16[/tex]So, we have: [tex]- * + = +\\- * - = +[/tex][tex]x ^ 2-8x + 16-x + 4-6 = 0[/tex]Equal signs add up and the same sign is placed. Different signs are subtracted and the sign of the major is placed. [tex]x ^ 2-9x + 14 = 0[/tex]Answer: [tex]x ^ 2-9x + 14 = 0[/tex]