(x+4)(2x+3)=(3x)(6-4x)+(2x+1)

Solution for (x+4)(2x+3)=(3x)(6-4x)+(2x+1) equation:

Simplifying
(x + 4)(2x + 3) = (3x)(6 + -4x) + (2x + 1)

Reorder the terms:
(4 + x)(2x + 3) = (3x)(6 + -4x) + (2x + 1)

Reorder the terms:
(4 + x)(3 + 2x) = (3x)(6 + -4x) + (2x + 1)

Multiply (4 + x) * (3 + 2x)
(4(3 + 2x) + x(3 + 2x)) = (3x)(6 + -4x) + (2x + 1)
((3 * 4 + 2x * 4) + x(3 + 2x)) = (3x)(6 + -4x) + (2x + 1)
((12 + 8x) + x(3 + 2x)) = (3x)(6 + -4x) + (2x + 1)
(12 + 8x + (3 * x + 2x * x)) = (3x)(6 + -4x) + (2x + 1)
(12 + 8x + (3x + 2x2)) = (3x)(6 + -4x) + (2x + 1)

Combine like terms: 8x + 3x = 11x
(12 + 11x + 2x2) = (3x)(6 + -4x) + (2x + 1)

Remove parenthesis around (3x)
12 + 11x + 2x2 = 3x(6 + -4x) + (2x + 1)
12 + 11x + 2x2 = (6 * 3x + -4x * 3x) + (2x + 1)
12 + 11x + 2x2 = (18x + -12x2) + (2x + 1)

Reorder the terms:
12 + 11x + 2x2 = 18x + -12x2 + (1 + 2x)

Remove parenthesis around (1 + 2x)
12 + 11x + 2x2 = 18x + -12x2 + 1 + 2x

Reorder the terms:
12 + 11x + 2x2 = 1 + 18x + 2x + -12x2

Combine like terms: 18x + 2x = 20x
12 + 11x + 2x2 = 1 + 20x + -12x2

Solving
12 + 11x + 2x2 = 1 + 20x + -12x2

Solving for variable 'x'.

Reorder the terms:
12 + -1 + 11x + -20x + 2x2 + 12x2 = 1 + 20x + -12x2 + -1 + -20x + 12x2

Combine like terms: 12 + -1 = 11
11 + 11x + -20x + 2x2 + 12x2 = 1 + 20x + -12x2 + -1 + -20x + 12x2

Combine like terms: 11x + -20x = -9x
11 + -9x + 2x2 + 12x2 = 1 + 20x + -12x2 + -1 + -20x + 12x2

Combine like terms: 2x2 + 12x2 = 14x2
11 + -9x + 14x2 = 1 + 20x + -12x2 + -1 + -20x + 12x2

Reorder the terms:
11 + -9x + 14x2 = 1 + -1 + 20x + -20x + -12x2 + 12x2

Combine like terms: 1 + -1 = 0
11 + -9x + 14x2 = 0 + 20x + -20x + -12x2 + 12x2
11 + -9x + 14x2 = 20x + -20x + -12x2 + 12x2

Combine like terms: 20x + -20x = 0
11 + -9x + 14x2 = 0 + -12x2 + 12x2
11 + -9x + 14x2 = -12x2 + 12x2

Combine like terms: -12x2 + 12x2 = 0
11 + -9x + 14x2 = 0

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

Divide each side by '14'.
0.7857142857 + -0.6428571429x + x2 = 0

Move the constant term to the right:

Add '-0.7857142857' to each side of the equation.
0.7857142857 + -0.6428571429x + -0.7857142857 + x2 = 0 + -0.7857142857

Reorder the terms:
0.7857142857 + -0.7857142857 + -0.6428571429x + x2 = 0 + -0.7857142857

Combine like terms: 0.7857142857 + -0.7857142857 = 0.0000000000
0.0000000000 + -0.6428571429x + x2 = 0 + -0.7857142857
-0.6428571429x + x2 = 0 + -0.7857142857

Combine like terms: 0 + -0.7857142857 = -0.7857142857
-0.6428571429x + x2 = -0.7857142857

The x term is -0.6428571429x.  Take half its coefficient (-0.3214285715).
Square it (0.1033163266) and add it to both sides.

Add '0.1033163266' to each side of the equation.
-0.6428571429x + 0.1033163266 + x2 = -0.7857142857 + 0.1033163266

Reorder the terms:
0.1033163266 + -0.6428571429x + x2 = -0.7857142857 + 0.1033163266

Combine like terms: -0.7857142857 + 0.1033163266 = -0.6823979591
0.1033163266 + -0.6428571429x + x2 = -0.6823979591

Factor a perfect square on the left side:
(x + -0.3214285715)(x + -0.3214285715) = -0.6823979591

Can't calculate square root of the right side.

The solution to this equation could not be determined.