(3-x)(x+4)+16=12x-(x+3)2

Solution for (3-x)(x+4)+16=12x-(x+3)2 equation:

Simplifying
(3 + -1x)(x + 4) + 16 = 12x + -1(x + 3) * 2

Reorder the terms:
(3 + -1x)(4 + x) + 16 = 12x + -1(x + 3) * 2

Multiply (3 + -1x) * (4 + x)
(3(4 + x) + -1x * (4 + x)) + 16 = 12x + -1(x + 3) * 2
((4 * 3 + x * 3) + -1x * (4 + x)) + 16 = 12x + -1(x + 3) * 2
((12 + 3x) + -1x * (4 + x)) + 16 = 12x + -1(x + 3) * 2
(12 + 3x + (4 * -1x + x * -1x)) + 16 = 12x + -1(x + 3) * 2
(12 + 3x + (-4x + -1x2)) + 16 = 12x + -1(x + 3) * 2

Combine like terms: 3x + -4x = -1x
(12 + -1x + -1x2) + 16 = 12x + -1(x + 3) * 2

Reorder the terms:
12 + 16 + -1x + -1x2 = 12x + -1(x + 3) * 2

Combine like terms: 12 + 16 = 28
28 + -1x + -1x2 = 12x + -1(x + 3) * 2

Reorder the terms:
28 + -1x + -1x2 = 12x + -1(3 + x) * 2

Reorder the terms for easier multiplication:
28 + -1x + -1x2 = 12x + -1 * 2(3 + x)

Multiply -1 * 2
28 + -1x + -1x2 = 12x + -2(3 + x)
28 + -1x + -1x2 = 12x + (3 * -2 + x * -2)
28 + -1x + -1x2 = 12x + (-6 + -2x)

Reorder the terms:
28 + -1x + -1x2 = -6 + 12x + -2x

Combine like terms: 12x + -2x = 10x
28 + -1x + -1x2 = -6 + 10x

Solving
28 + -1x + -1x2 = -6 + 10x

Solving for variable 'x'.

Reorder the terms:
28 + 6 + -1x + -10x + -1x2 = -6 + 10x + 6 + -10x

Combine like terms: 28 + 6 = 34
34 + -1x + -10x + -1x2 = -6 + 10x + 6 + -10x

Combine like terms: -1x + -10x = -11x
34 + -11x + -1x2 = -6 + 10x + 6 + -10x

Reorder the terms:
34 + -11x + -1x2 = -6 + 6 + 10x + -10x

Combine like terms: -6 + 6 = 0
34 + -11x + -1x2 = 0 + 10x + -10x
34 + -11x + -1x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
34 + -11x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-34 + 11x + x2 = 0

Move the constant term to the right:

Add '34' to each side of the equation.
-34 + 11x + 34 + x2 = 0 + 34

Reorder the terms:
-34 + 34 + 11x + x2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + 11x + x2 = 0 + 34
11x + x2 = 0 + 34

Combine like terms: 0 + 34 = 34
11x + x2 = 34

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 34 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 34 + 30.25

Combine like terms: 34 + 30.25 = 64.25
30.25 + 11x + x2 = 64.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 64.25

Calculate the square root of the right side: 8.015609771

Break this problem into two subproblems by setting 
(x + 5.5) equal to 8.015609771 and -8.015609771.

Subproblem 1
x + 5.5 = 8.015609771

Simplifying
x + 5.5 = 8.015609771

Reorder the terms:
5.5 + x = 8.015609771

Solving
5.5 + x = 8.015609771

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 8.015609771 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 8.015609771 + -5.5
x = 8.015609771 + -5.5

Combine like terms: 8.015609771 + -5.5 = 2.515609771
x = 2.515609771

Simplifying
x = 2.515609771

Subproblem 2
x + 5.5 = -8.015609771

Simplifying
x + 5.5 = -8.015609771

Reorder the terms:
5.5 + x = -8.015609771

Solving
5.5 + x = -8.015609771

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -8.015609771 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -8.015609771 + -5.5
x = -8.015609771 + -5.5

Combine like terms: -8.015609771 + -5.5 = -13.515609771
x = -13.515609771

Simplifying
x = -13.515609771

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.515609771, -13.515609771}