The equation to be solved is (2x+1)(3x-2)=55

(2x+1)(3x-2)=55

=> 6x^2 - x - 2 = 55

=> 6x^2 - x - 57 = 0

=> 6x^2 - 19x + 18x - 57 = 0

=> x(6x - 19) + 3(6x - 19) = 0

=> (x + 3)(6x - 19) = 0

x = -3 and x = 19/6

**The roots of the equation are (-3 , 19/6)**

To solve the equation (2x+1)(3x-2)=55, expand the expression on the left. This leads to a quadratic equation which can then be solved to give the required value of x.

(2x+1)(3x-2)=55

6x^2 + 3x - 4x - 2 = 55

6x^2 - x - 57 = 0

6x^2 + 18x - 19x - 57 = 0

6x(x + 3) - 19(x + 3) = 0

(6x - 19)(x +3) = 0

x = 19/6 and x = -3

The solution of the given equation is x = -3 and x = 19/6

(2x+1)(3x-2)=55

2x(3x-2) + 1*(3x-2) = 55

2x*3x - 2x*2 + 1*3x - 1*2 = 55

6x^2 - 4x + 3x - 2 = 55

6x^2 - x - 2 = 55

We'll shift 55 to the left:

6x^2 - x - 2 - 55 = 0

6x^2 - x - 57 = 0

We'll apply the quadratic formula:

x1 = [1 + sqrt(1 + 24*57)]/12

x1 = (1 + sqrt1369)/12

x1 = (1 + 37)/12

x1 = 38/12

x1 = 19/6

x2 = (1-37)/12

x2 = -36/12

x2 = -3

**The required solutions of the equation are: {-3 ; 19/6}.**