(2x)(x+12)=32

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Solution for (2x)(x+12)=32 equation: 


Simplifying
(2x)(x + 12) = 32

Remove parenthesis around (2x)
2x(x + 12) = 32

Reorder the terms:
2x(12 + x) = 32
(12 * 2x + x * 2x) = 32
(24x + 2x2) = 32

Solving
24x + 2x2 = 32

Solving for variable 'x'.

Reorder the terms:
-32 + 24x + 2x2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + 24x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + 12x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-16 + 12x + x2)' equal to zero and attempt to solve:

Simplifying
-16 + 12x + x2 = 0

Solving
-16 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 12x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 12x + x2 = 0 + 16

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

Combine like terms: 0 + 16 = 16
12x + x2 = 16

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 16 + 36

Reorder the terms:
36 + 12x + x2 = 16 + 36

Combine like terms: 16 + 36 = 52
36 + 12x + x2 = 52

Factor a perfect square on the left side:
(x + 6)(x + 6) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(x + 6) equal to 7.211102551 and -7.211102551.


Subproblem 1
x + 6 = 7.211102551

Simplifying
x + 6 = 7.211102551

Reorder the terms:
6 + x = 7.211102551

Solving
6 + x = 7.211102551

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 7.211102551 + -6

Combine like terms: 6 + -6 = 0
0 + x = 7.211102551 + -6
x = 7.211102551 + -6

Combine like terms: 7.211102551 + -6 = 1.211102551
x = 1.211102551

Simplifying
x = 1.211102551


Subproblem 2
x + 6 = -7.211102551

Simplifying
x + 6 = -7.211102551

Reorder the terms:
6 + x = -7.211102551

Solving
6 + x = -7.211102551

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -7.211102551 + -6

Combine like terms: 6 + -6 = 0
0 + x = -7.211102551 + -6
x = -7.211102551 + -6

Combine like terms: -7.211102551 + -6 = -13.211102551
x = -13.211102551

Simplifying
x = -13.211102551


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.211102551, -13.211102551}
Solution
x = {1.211102551, -13.211102551}

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