12(2x+1)=4x^2+4x

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Solution for 12(2x+1)=4x^2+4x equation: 


Simplifying
12(2x + 1) = 4x2 + 4x

Reorder the terms:
12(1 + 2x) = 4x2 + 4x
(1 * 12 + 2x * 12) = 4x2 + 4x
(12 + 24x) = 4x2 + 4x

Reorder the terms:
12 + 24x = 4x + 4x2

Solving
12 + 24x = 4x + 4x2

Solving for variable 'x'.

Combine like terms: 24x + -4x = 20x
12 + 20x + -4x2 = 4x + 4x2 + -4x + -4x2

Reorder the terms:
12 + 20x + -4x2 = 4x + -4x + 4x2 + -4x2

Combine like terms: 4x + -4x = 0
12 + 20x + -4x2 = 0 + 4x2 + -4x2
12 + 20x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
12 + 20x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 5x + -1x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(3 + 5x + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + 5x + -1x2 = 0

Solving
3 + 5x + -1x2 = 0

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

Divide each side by '-1'.
-3 + -5x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -5x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -5x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5x + x2 = 0 + 3
-5x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-5x + x2 = 3

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 = 3 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 3 + 6.25

Combine like terms: 3 + 6.25 = 9.25
6.25 + -5x + x2 = 9.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(x + -2.5) equal to 3.041381265 and -3.041381265.


Subproblem 1
x + -2.5 = 3.041381265

Simplifying
x + -2.5 = 3.041381265

Reorder the terms:
-2.5 + x = 3.041381265

Solving
-2.5 + x = 3.041381265

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 = 3.041381265 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 3.041381265 + 2.5
x = 3.041381265 + 2.5

Combine like terms: 3.041381265 + 2.5 = 5.541381265
x = 5.541381265

Simplifying
x = 5.541381265


Subproblem 2
x + -2.5 = -3.041381265

Simplifying
x + -2.5 = -3.041381265

Reorder the terms:
-2.5 + x = -3.041381265

Solving
-2.5 + x = -3.041381265

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 = -3.041381265 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -3.041381265 + 2.5
x = -3.041381265 + 2.5

Combine like terms: -3.041381265 + 2.5 = -0.541381265
x = -0.541381265

Simplifying
x = -0.541381265


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.541381265, -0.541381265}
Solution
x = {5.541381265, -0.541381265}

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