12x(x+4)=4(1+3x)

Solution for 12x(x+4)=4(1+3x) equation:

Simplifying
12x(x + 4) = 4(1 + 3x)

Reorder the terms:
12x(4 + x) = 4(1 + 3x)
(4 * 12x + x * 12x) = 4(1 + 3x)
(48x + 12x2) = 4(1 + 3x)
48x + 12x2 = (1 * 4 + 3x * 4)
48x + 12x2 = (4 + 12x)

Solving
48x + 12x2 = 4 + 12x

Solving for variable 'x'.

Reorder the terms:
-4 + 48x + -12x + 12x2 = 4 + 12x + -4 + -12x

Combine like terms: 48x + -12x = 36x
-4 + 36x + 12x2 = 4 + 12x + -4 + -12x

Reorder the terms:
-4 + 36x + 12x2 = 4 + -4 + 12x + -12x

Combine like terms: 4 + -4 = 0
-4 + 36x + 12x2 = 0 + 12x + -12x
-4 + 36x + 12x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-4 + 36x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 9x + 3x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + 9x + 3x2)' equal to zero and attempt to solve:

Simplifying
-1 + 9x + 3x2 = 0

Solving
-1 + 9x + 3x2 = 0

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

Divide each side by '3'.
-0.3333333333 + 3x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 3x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 3x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 3x + x2 = 0 + 0.3333333333
3x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
3x + x2 = 0.3333333333

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 = 0.3333333333 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 0.3333333333 + 2.25

Combine like terms: 0.3333333333 + 2.25 = 2.5833333333
2.25 + 3x + x2 = 2.5833333333

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 2.5833333333

Calculate the square root of the right side: 1.607275127

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.607275127 and -1.607275127.

Subproblem 1
x + 1.5 = 1.607275127

Simplifying
x + 1.5 = 1.607275127

Reorder the terms:
1.5 + x = 1.607275127

Solving
1.5 + x = 1.607275127

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 = 1.607275127 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 1.607275127 + -1.5
x = 1.607275127 + -1.5

Combine like terms: 1.607275127 + -1.5 = 0.107275127
x = 0.107275127

Simplifying
x = 0.107275127

Subproblem 2
x + 1.5 = -1.607275127

Simplifying
x + 1.5 = -1.607275127

Reorder the terms:
1.5 + x = -1.607275127

Solving
1.5 + x = -1.607275127

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 = -1.607275127 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -1.607275127 + -1.5
x = -1.607275127 + -1.5

Combine like terms: -1.607275127 + -1.5 = -3.107275127
x = -3.107275127

Simplifying
x = -3.107275127

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.107275127, -3.107275127}
Solution
x = {0.107275127, -3.107275127}