The left side is (trace my transformations)

      (x+1)*(x-2) + (x+2)(x+1) = take the common factor (x+1) out the parenteses = 

    = (x+1)*(x-2 + x+2) = (x+1)*(2x).



So, the equation takes the form

    2x*(x+1) = 2*(3x-1)


Cancel common factor 2 in both sides

    x*(x+1) = 3x-1


Simplify

    x^2 + x = 3x -1

    x^2 - 2x + 1 = 0

    (x-1)^2 = 0


The only solution is  x= 1.


ANSWER.  The given equation has a unique solution x= 1.