2x+3x(x-6)+12=x^2+16

Solution for 2x+3x(x-6)+12=x^2+16 equation:

Simplifying
2x + 3x(x + -6) + 12 = x2 + 16

Reorder the terms:
2x + 3x(-6 + x) + 12 = x2 + 16
2x + (-6 * 3x + x * 3x) + 12 = x2 + 16
2x + (-18x + 3x2) + 12 = x2 + 16

Reorder the terms:
12 + 2x + -18x + 3x2 = x2 + 16

Combine like terms: 2x + -18x = -16x
12 + -16x + 3x2 = x2 + 16

Reorder the terms:
12 + -16x + 3x2 = 16 + x2

Solving
12 + -16x + 3x2 = 16 + x2

Solving for variable 'x'.

Reorder the terms:
12 + -16 + -16x + 3x2 + -1x2 = 16 + x2 + -16 + -1x2

Combine like terms: 12 + -16 = -4
-4 + -16x + 3x2 + -1x2 = 16 + x2 + -16 + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
-4 + -16x + 2x2 = 16 + x2 + -16 + -1x2

Reorder the terms:
-4 + -16x + 2x2 = 16 + -16 + x2 + -1x2

Combine like terms: 16 + -16 = 0
-4 + -16x + 2x2 = 0 + x2 + -1x2
-4 + -16x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + -16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -8x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
-2 + -8x + x2 = 0

Solving
-2 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -8x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -8x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -8x + x2 = 0 + 2
-8x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-8x + x2 = 2

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 2 + 16

Reorder the terms:
16 + -8x + x2 = 2 + 16

Combine like terms: 2 + 16 = 18
16 + -8x + x2 = 18

Factor a perfect square on the left side:
(x + -4)(x + -4) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + -4) equal to 4.242640687 and -4.242640687.

Subproblem 1
x + -4 = 4.242640687

Simplifying
x + -4 = 4.242640687

Reorder the terms:
-4 + x = 4.242640687

Solving
-4 + x = 4.242640687

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 4.242640687 + 4

Combine like terms: -4 + 4 = 0
0 + x = 4.242640687 + 4
x = 4.242640687 + 4

Combine like terms: 4.242640687 + 4 = 8.242640687
x = 8.242640687

Simplifying
x = 8.242640687

Subproblem 2
x + -4 = -4.242640687

Simplifying
x + -4 = -4.242640687

Reorder the terms:
-4 + x = -4.242640687

Solving
-4 + x = -4.242640687

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -4.242640687 + 4

Combine like terms: -4 + 4 = 0
0 + x = -4.242640687 + 4
x = -4.242640687 + 4

Combine like terms: -4.242640687 + 4 = -0.242640687
x = -0.242640687

Simplifying
x = -0.242640687

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.242640687, -0.242640687}
Solution
x = {8.242640687, -0.242640687}