Solve x^2-5x+6=0

To solve this, we need to factorise the expression (write as a product of two brackets). To do this we want to find to numbers that multiply to make +6 and add up to -5, for this case. These numbers turn out to be -2 and -3. Hence, we can write the expression as (x-2)(x-3)=0 (check with "smiley face" method). This means that either x-2=0 or x-3 =0. So by rearranging, we find that x=2 or x=3.