2x(x+16)+4=6(x+3)-12

Solution for 2x(x+16)+4=6(x+3)-12 equation:

Simplifying
2x(x + 16) + 4 = 6(x + 3) + -12

Reorder the terms:
2x(16 + x) + 4 = 6(x + 3) + -12
(16 * 2x + x * 2x) + 4 = 6(x + 3) + -12
(32x + 2x2) + 4 = 6(x + 3) + -12

Reorder the terms:
4 + 32x + 2x2 = 6(x + 3) + -12

Reorder the terms:
4 + 32x + 2x2 = 6(3 + x) + -12
4 + 32x + 2x2 = (3 * 6 + x * 6) + -12
4 + 32x + 2x2 = (18 + 6x) + -12

Reorder the terms:
4 + 32x + 2x2 = 18 + -12 + 6x

Combine like terms: 18 + -12 = 6
4 + 32x + 2x2 = 6 + 6x

Solving
4 + 32x + 2x2 = 6 + 6x

Solving for variable 'x'.

Reorder the terms:
4 + -6 + 32x + -6x + 2x2 = 6 + 6x + -6 + -6x

Combine like terms: 4 + -6 = -2
-2 + 32x + -6x + 2x2 = 6 + 6x + -6 + -6x

Combine like terms: 32x + -6x = 26x
-2 + 26x + 2x2 = 6 + 6x + -6 + -6x

Reorder the terms:
-2 + 26x + 2x2 = 6 + -6 + 6x + -6x

Combine like terms: 6 + -6 = 0
-2 + 26x + 2x2 = 0 + 6x + -6x
-2 + 26x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-2 + 26x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 13x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 13x + x2)' equal to zero and attempt to solve:

Simplifying
-1 + 13x + x2 = 0

Solving
-1 + 13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 13x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 13x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 13x + x2 = 0 + 1
13x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
13x + x2 = 1

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = 1 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 1 + 42.25

Combine like terms: 1 + 42.25 = 43.25
42.25 + 13x + x2 = 43.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 43.25

Calculate the square root of the right side: 6.576473219

Break this problem into two subproblems by setting 
(x + 6.5) equal to 6.576473219 and -6.576473219.

Subproblem 1
x + 6.5 = 6.576473219

Simplifying
x + 6.5 = 6.576473219

Reorder the terms:
6.5 + x = 6.576473219

Solving
6.5 + x = 6.576473219

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = 6.576473219 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 6.576473219 + -6.5
x = 6.576473219 + -6.5

Combine like terms: 6.576473219 + -6.5 = 0.076473219
x = 0.076473219

Simplifying
x = 0.076473219

Subproblem 2
x + 6.5 = -6.576473219

Simplifying
x + 6.5 = -6.576473219

Reorder the terms:
6.5 + x = -6.576473219

Solving
6.5 + x = -6.576473219

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = -6.576473219 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -6.576473219 + -6.5
x = -6.576473219 + -6.5

Combine like terms: -6.576473219 + -6.5 = -13.076473219
x = -13.076473219

Simplifying
x = -13.076473219

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.076473219, -13.076473219}
Solution
x = {0.076473219, -13.076473219}