(3x+1)(2x+3)+3=0

Solution for (3x+1)(2x+3)+3=0 equation:

Simplifying
(3x + 1)(2x + 3) + 3 = 0

Reorder the terms:
(1 + 3x)(2x + 3) + 3 = 0

Reorder the terms:
(1 + 3x)(3 + 2x) + 3 = 0

Multiply (1 + 3x) * (3 + 2x)
(1(3 + 2x) + 3x * (3 + 2x)) + 3 = 0
((3 * 1 + 2x * 1) + 3x * (3 + 2x)) + 3 = 0
((3 + 2x) + 3x * (3 + 2x)) + 3 = 0
(3 + 2x + (3 * 3x + 2x * 3x)) + 3 = 0
(3 + 2x + (9x + 6x2)) + 3 = 0

Combine like terms: 2x + 9x = 11x
(3 + 11x + 6x2) + 3 = 0

Reorder the terms:
3 + 3 + 11x + 6x2 = 0

Combine like terms: 3 + 3 = 6
6 + 11x + 6x2 = 0

Solving
6 + 11x + 6x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
1 + 1.833333333x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 1.833333333x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 1.833333333x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 1.833333333x + x2 = 0 + -1
1.833333333x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
1.833333333x + x2 = -1

The x term is 1.833333333x.  Take half its coefficient (0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
1.833333333x + 0.8402777775 + x2 = -1 + 0.8402777775

Reorder the terms:
0.8402777775 + 1.833333333x + x2 = -1 + 0.8402777775

Combine like terms: -1 + 0.8402777775 = -0.1597222225
0.8402777775 + 1.833333333x + x2 = -0.1597222225

Factor a perfect square on the left side:
(x + 0.9166666665)(x + 0.9166666665) = -0.1597222225

Can't calculate square root of the right side.

The solution to this equation could not be determined.