(x+2)*6x=126

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Solution for (x+2)*6x=126 equation: 


Simplifying
(x + 2) * 6x = 126

Reorder the terms:
(2 + x) * 6x = 126

Reorder the terms for easier multiplication:
6x(2 + x) = 126
(2 * 6x + x * 6x) = 126
(12x + 6x2) = 126

Solving
12x + 6x2 = 126

Solving for variable 'x'.

Reorder the terms:
-126 + 12x + 6x2 = 126 + -126

Combine like terms: 126 + -126 = 0
-126 + 12x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-21 + 2x + x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-21 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-21 + 2x + x2 = 0

Solving
-21 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 2x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + 2x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 2x + x2 = 0 + 21
2x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
2x + x2 = 21

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 21 + 1

Reorder the terms:
1 + 2x + x2 = 21 + 1

Combine like terms: 21 + 1 = 22
1 + 2x + x2 = 22

Factor a perfect square on the left side:
(x + 1)(x + 1) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(x + 1) equal to 4.69041576 and -4.69041576.


Subproblem 1
x + 1 = 4.69041576

Simplifying
x + 1 = 4.69041576

Reorder the terms:
1 + x = 4.69041576

Solving
1 + x = 4.69041576

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 4.69041576 + -1

Combine like terms: 1 + -1 = 0
0 + x = 4.69041576 + -1
x = 4.69041576 + -1

Combine like terms: 4.69041576 + -1 = 3.69041576
x = 3.69041576

Simplifying
x = 3.69041576


Subproblem 2
x + 1 = -4.69041576

Simplifying
x + 1 = -4.69041576

Reorder the terms:
1 + x = -4.69041576

Solving
1 + x = -4.69041576

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -4.69041576 + -1

Combine like terms: 1 + -1 = 0
0 + x = -4.69041576 + -1
x = -4.69041576 + -1

Combine like terms: -4.69041576 + -1 = -5.69041576
x = -5.69041576

Simplifying
x = -5.69041576


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.69041576, -5.69041576}
Solution
x = {3.69041576, -5.69041576}

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