Given: x2 –5x + 6 = 0
On splitting the middle term –5x as – 3x – 2x, we get:
x2 – 3x – 2x + 6 = 0
x(x – 3) – 2(x – 3) = 0
(x – 3) (x – 2) = 0
We know that if the product of two numbers is zero, then at least one of them must be zero.
Thus,
x – 3 = 0 or x – 2 = 0
x = 3 or x = 2
Therefore, the solution of the given equation is x = 3, 2.