(x²-5x+6)(x²-5x-4)+16=0
(x²-5x)²-4(x²-5x)+6(x²-5x)-24+16=0
(x²-5x)²+2(x²-5x)-8=0
(x²-5x+4)(x²-5x-2)=0
则可得x²-5x+4=0或x²-5x-2=0
由x²-5x+4=0得 (x-1)(x-4)=0,解得x1=2,x2=4
由x²-5x-2=0得 (x-5/2)²=33/4,解得x3=(5+√33)/2 ,x4=(5-√33)/2
综上: 方程(x^2-5x+6)(x^2-5x-4)+16=0的解为x1=2,x2=4,x3=(5+√33)/2 ,x4=(5-√33)/2