252=(x+2)(x)(2)

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Solution for 252=(x+2)(x)(2) equation: 


Simplifying
252 = (x + 2)(x)(2)

Reorder the terms:
252 = (2 + x)(x)(2)

Reorder the terms for easier multiplication:
252 = 2x(2 + x)
252 = (2 * 2x + x * 2x)
252 = (4x + 2x2)

Solving
252 = 4x + 2x2

Solving for variable 'x'.

Reorder the terms:
252 + -4x + -2x2 = 4x + -4x + 2x2 + -2x2

Combine like terms: 4x + -4x = 0
252 + -4x + -2x2 = 0 + 2x2 + -2x2
252 + -4x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
252 + -4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(126 + -2x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(126 + -2x + -1x2)' equal to zero and attempt to solve:

Simplifying
126 + -2x + -1x2 = 0

Solving
126 + -2x + -1x2 = 0

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

Divide each side by '-1'.
-126 + 2x + x2 = 0

Move the constant term to the right:

Add '126' to each side of the equation.
-126 + 2x + 126 + x2 = 0 + 126

Reorder the terms:
-126 + 126 + 2x + x2 = 0 + 126

Combine like terms: -126 + 126 = 0
0 + 2x + x2 = 0 + 126
2x + x2 = 0 + 126

Combine like terms: 0 + 126 = 126
2x + x2 = 126

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 = 126 + 1

Reorder the terms:
1 + 2x + x2 = 126 + 1

Combine like terms: 126 + 1 = 127
1 + 2x + x2 = 127

Factor a perfect square on the left side:
(x + 1)(x + 1) = 127

Calculate the square root of the right side: 11.26942767

Break this problem into two subproblems by setting 
(x + 1) equal to 11.26942767 and -11.26942767.


Subproblem 1
x + 1 = 11.26942767

Simplifying
x + 1 = 11.26942767

Reorder the terms:
1 + x = 11.26942767

Solving
1 + x = 11.26942767

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 = 11.26942767 + -1

Combine like terms: 1 + -1 = 0
0 + x = 11.26942767 + -1
x = 11.26942767 + -1

Combine like terms: 11.26942767 + -1 = 10.26942767
x = 10.26942767

Simplifying
x = 10.26942767


Subproblem 2
x + 1 = -11.26942767

Simplifying
x + 1 = -11.26942767

Reorder the terms:
1 + x = -11.26942767

Solving
1 + x = -11.26942767

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 = -11.26942767 + -1

Combine like terms: 1 + -1 = 0
0 + x = -11.26942767 + -1
x = -11.26942767 + -1

Combine like terms: -11.26942767 + -1 = -12.26942767
x = -12.26942767

Simplifying
x = -12.26942767


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.26942767, -12.26942767}
Solution
x = {10.26942767, -12.26942767}

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