12x(4+x)=12+4

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

Simplifying
12x(4 + x) = 12 + 4
(4 * 12x + x * 12x) = 12 + 4
(48x + 12x2) = 12 + 4

Combine like terms: 12 + 4 = 16
48x + 12x2 = 16

Solving
48x + 12x2 = 16

Solving for variable 'x'.

Reorder the terms:
-16 + 48x + 12x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 48x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + 12x + 3x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-4 + 12x + 3x2)' equal to zero and attempt to solve:

Simplifying
-4 + 12x + 3x2 = 0

Solving
-4 + 12x + 3x2 = 0

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

Divide each side by '3'.
-1.333333333 + 4x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 4x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 4x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 4x + x2 = 0 + 1.333333333
4x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
4x + x2 = 1.333333333

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 1.333333333 + 4

Reorder the terms:
4 + 4x + x2 = 1.333333333 + 4

Combine like terms: 1.333333333 + 4 = 5.333333333
4 + 4x + x2 = 5.333333333

Factor a perfect square on the left side:
(x + 2)(x + 2) = 5.333333333

Calculate the square root of the right side: 2.309401077

Break this problem into two subproblems by setting 
(x + 2) equal to 2.309401077 and -2.309401077.

Subproblem 1
x + 2 = 2.309401077

Simplifying
x + 2 = 2.309401077

Reorder the terms:
2 + x = 2.309401077

Solving
2 + x = 2.309401077

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 2.309401077 + -2

Combine like terms: 2 + -2 = 0
0 + x = 2.309401077 + -2
x = 2.309401077 + -2

Combine like terms: 2.309401077 + -2 = 0.309401077
x = 0.309401077

Simplifying
x = 0.309401077

Subproblem 2
x + 2 = -2.309401077

Simplifying
x + 2 = -2.309401077

Reorder the terms:
2 + x = -2.309401077

Solving
2 + x = -2.309401077

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -2.309401077 + -2

Combine like terms: 2 + -2 = 0
0 + x = -2.309401077 + -2
x = -2.309401077 + -2

Combine like terms: -2.309401077 + -2 = -4.309401077
x = -4.309401077

Simplifying
x = -4.309401077

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.309401077, -4.309401077}
Solution
x = {0.309401077, -4.309401077}