x=(x-2)*(x+6)

Solution for x=(x-2)*(x+6) equation:

Simplifying
x = (x + -2)(x + 6)

Reorder the terms:
x = (-2 + x)(x + 6)

Reorder the terms:
x = (-2 + x)(6 + x)

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

Combine like terms: -2x + 6x = 4x
x = (-12 + 4x + x2)

Solving
x = -12 + 4x + x2

Solving for variable 'x'.

Reorder the terms:
12 + x + -4x + -1x2 = -12 + 4x + x2 + 12 + -4x + -1x2

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

Reorder the terms:
12 + -3x + -1x2 = -12 + 12 + 4x + -4x + x2 + -1x2

Combine like terms: -12 + 12 = 0
12 + -3x + -1x2 = 0 + 4x + -4x + x2 + -1x2
12 + -3x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
12 + -3x + -1x2 = 0 + x2 + -1x2
12 + -3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + -3x + -1x2 = 0

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

Divide each side by '-1'.
-12 + 3x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 3x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 3x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 3x + x2 = 0 + 12
3x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
3x + x2 = 12

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 12 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 12 + 2.25

Combine like terms: 12 + 2.25 = 14.25
2.25 + 3x + x2 = 14.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.774917218 and -3.774917218.

Subproblem 1
x + 1.5 = 3.774917218

Simplifying
x + 1.5 = 3.774917218

Reorder the terms:
1.5 + x = 3.774917218

Solving
1.5 + x = 3.774917218

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 3.774917218 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 3.774917218 + -1.5
x = 3.774917218 + -1.5

Combine like terms: 3.774917218 + -1.5 = 2.274917218
x = 2.274917218

Simplifying
x = 2.274917218

Subproblem 2
x + 1.5 = -3.774917218

Simplifying
x + 1.5 = -3.774917218

Reorder the terms:
1.5 + x = -3.774917218

Solving
1.5 + x = -3.774917218

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -3.774917218 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -3.774917218 + -1.5
x = -3.774917218 + -1.5

Combine like terms: -3.774917218 + -1.5 = -5.274917218
x = -5.274917218

Simplifying
x = -5.274917218

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.274917218, -5.274917218}