(14-2x)(x+2)=12

Solution for (14-2x)(x+2)=12 equation:

Simplifying
(14 + -2x)(x + 2) = 12

Reorder the terms:
(14 + -2x)(2 + x) = 12

Multiply (14 + -2x) * (2 + x)
(14(2 + x) + -2x * (2 + x)) = 12
((2 * 14 + x * 14) + -2x * (2 + x)) = 12
((28 + 14x) + -2x * (2 + x)) = 12
(28 + 14x + (2 * -2x + x * -2x)) = 12
(28 + 14x + (-4x + -2x2)) = 12

Combine like terms: 14x + -4x = 10x
(28 + 10x + -2x2) = 12

Solving
28 + 10x + -2x2 = 12

Solving for variable 'x'.

Reorder the terms:
28 + -12 + 10x + -2x2 = 12 + -12

Combine like terms: 28 + -12 = 16
16 + 10x + -2x2 = 12 + -12

Combine like terms: 12 + -12 = 0
16 + 10x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 5x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + 5x + -1x2)' equal to zero and attempt to solve:

Simplifying
8 + 5x + -1x2 = 0

Solving
8 + 5x + -1x2 = 0

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

Divide each side by '-1'.
-8 + -5x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -5x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -5x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -5x + x2 = 0 + 8
-5x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-5x + x2 = 8

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 8 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 8 + 6.25

Combine like terms: 8 + 6.25 = 14.25
6.25 + -5x + x2 = 14.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + -2.5) equal to 3.774917218 and -3.774917218.

Subproblem 1
x + -2.5 = 3.774917218

Simplifying
x + -2.5 = 3.774917218

Reorder the terms:
-2.5 + x = 3.774917218

Solving
-2.5 + x = 3.774917218

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 3.774917218 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 3.774917218 + 2.5
x = 3.774917218 + 2.5

Combine like terms: 3.774917218 + 2.5 = 6.274917218
x = 6.274917218

Simplifying
x = 6.274917218

Subproblem 2
x + -2.5 = -3.774917218

Simplifying
x + -2.5 = -3.774917218

Reorder the terms:
-2.5 + x = -3.774917218

Solving
-2.5 + x = -3.774917218

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -3.774917218 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -3.774917218 + 2.5
x = -3.774917218 + 2.5

Combine like terms: -3.774917218 + 2.5 = -1.274917218
x = -1.274917218

Simplifying
x = -1.274917218

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.274917218, -1.274917218}
Solution
x = {6.274917218, -1.274917218}