(x+4)(2x+3)=(3x)(12-4x)+(2x+1)

Solution for (x+4)(2x+3)=(3x)(12-4x)+(2x+1) equation:

Simplifying
(x + 4)(2x + 3) = (3x)(12 + -4x) + (2x + 1)

Reorder the terms:
(4 + x)(2x + 3) = (3x)(12 + -4x) + (2x + 1)

Reorder the terms:
(4 + x)(3 + 2x) = (3x)(12 + -4x) + (2x + 1)

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

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

Remove parenthesis around (3x)
12 + 11x + 2x2 = 3x(12 + -4x) + (2x + 1)
12 + 11x + 2x2 = (12 * 3x + -4x * 3x) + (2x + 1)
12 + 11x + 2x2 = (36x + -12x2) + (2x + 1)

Reorder the terms:
12 + 11x + 2x2 = 36x + -12x2 + (1 + 2x)

Remove parenthesis around (1 + 2x)
12 + 11x + 2x2 = 36x + -12x2 + 1 + 2x

Reorder the terms:
12 + 11x + 2x2 = 1 + 36x + 2x + -12x2

Combine like terms: 36x + 2x = 38x
12 + 11x + 2x2 = 1 + 38x + -12x2

Solving
12 + 11x + 2x2 = 1 + 38x + -12x2

Solving for variable 'x'.

Reorder the terms:
12 + -1 + 11x + -38x + 2x2 + 12x2 = 1 + 38x + -12x2 + -1 + -38x + 12x2

Combine like terms: 12 + -1 = 11
11 + 11x + -38x + 2x2 + 12x2 = 1 + 38x + -12x2 + -1 + -38x + 12x2

Combine like terms: 11x + -38x = -27x
11 + -27x + 2x2 + 12x2 = 1 + 38x + -12x2 + -1 + -38x + 12x2

Combine like terms: 2x2 + 12x2 = 14x2
11 + -27x + 14x2 = 1 + 38x + -12x2 + -1 + -38x + 12x2

Reorder the terms:
11 + -27x + 14x2 = 1 + -1 + 38x + -38x + -12x2 + 12x2

Combine like terms: 1 + -1 = 0
11 + -27x + 14x2 = 0 + 38x + -38x + -12x2 + 12x2
11 + -27x + 14x2 = 38x + -38x + -12x2 + 12x2

Combine like terms: 38x + -38x = 0
11 + -27x + 14x2 = 0 + -12x2 + 12x2
11 + -27x + 14x2 = -12x2 + 12x2

Combine like terms: -12x2 + 12x2 = 0
11 + -27x + 14x2 = 0

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

Divide each side by '14'.
0.7857142857 + -1.928571429x + x2 = 0

Move the constant term to the right:

Add '-0.7857142857' to each side of the equation.
0.7857142857 + -1.928571429x + -0.7857142857 + x2 = 0 + -0.7857142857

Reorder the terms:
0.7857142857 + -0.7857142857 + -1.928571429x + x2 = 0 + -0.7857142857

Combine like terms: 0.7857142857 + -0.7857142857 = 0.0000000000
0.0000000000 + -1.928571429x + x2 = 0 + -0.7857142857
-1.928571429x + x2 = 0 + -0.7857142857

Combine like terms: 0 + -0.7857142857 = -0.7857142857
-1.928571429x + x2 = -0.7857142857

The x term is -1.928571429x.  Take half its coefficient (-0.9642857145).
Square it (0.9298469392) and add it to both sides.

Add '0.9298469392' to each side of the equation.
-1.928571429x + 0.9298469392 + x2 = -0.7857142857 + 0.9298469392

Reorder the terms:
0.9298469392 + -1.928571429x + x2 = -0.7857142857 + 0.9298469392

Combine like terms: -0.7857142857 + 0.9298469392 = 0.1441326535
0.9298469392 + -1.928571429x + x2 = 0.1441326535

Factor a perfect square on the left side:
(x + -0.9642857145)(x + -0.9642857145) = 0.1441326535

Calculate the square root of the right side: 0.379648065

Break this problem into two subproblems by setting 
(x + -0.9642857145) equal to 0.379648065 and -0.379648065.

Subproblem 1
x + -0.9642857145 = 0.379648065

Simplifying
x + -0.9642857145 = 0.379648065

Reorder the terms:
-0.9642857145 + x = 0.379648065

Solving
-0.9642857145 + x = 0.379648065

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.9642857145' to each side of the equation.
-0.9642857145 + 0.9642857145 + x = 0.379648065 + 0.9642857145

Combine like terms: -0.9642857145 + 0.9642857145 = 0.0000000000
0.0000000000 + x = 0.379648065 + 0.9642857145
x = 0.379648065 + 0.9642857145

Combine like terms: 0.379648065 + 0.9642857145 = 1.3439337795
x = 1.3439337795

Simplifying
x = 1.3439337795

Subproblem 2
x + -0.9642857145 = -0.379648065

Simplifying
x + -0.9642857145 = -0.379648065

Reorder the terms:
-0.9642857145 + x = -0.379648065

Solving
-0.9642857145 + x = -0.379648065

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.9642857145' to each side of the equation.
-0.9642857145 + 0.9642857145 + x = -0.379648065 + 0.9642857145

Combine like terms: -0.9642857145 + 0.9642857145 = 0.0000000000
0.0000000000 + x = -0.379648065 + 0.9642857145
x = -0.379648065 + 0.9642857145

Combine like terms: -0.379648065 + 0.9642857145 = 0.5846376495
x = 0.5846376495

Simplifying
x = 0.5846376495

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.3439337795, 0.5846376495}