|x2−5x+6|+|x2−8x+12|=0
Every modulus is a non negative number and if two non negative numbers add up to get zero, then individual numbers itself equal to zero simultaneously.
∴x2−5x+6=0⇒(x−2)(x−3)=0⇒x=2,3
and x2−8x+12=0
⇒(x−2)(x−6)=0⇒x=2,6
Both the equations are zero at x=2
Hence, x=2 is the only solution for the equation.