Try factoring the quadratic by getting the roots through the quadratic formula.
Why in the world would you first multiply and then factor? You start with so obviously, one factor is x- 2. In order to factor into factors with integer coefficients, I would note that 5 factors only as 1(5) but neither 5-1 nor 5+ 1 is equal to 2 so we can't factor with integer coefficients. Not every quadratic can be factored with integer (or even real) coefficients.
So instead, complete the square! so that . Now use the identity .