(12x+4)(12x+4)=42

Solution for (12x+4)(12x+4)=42 equation:

Simplifying
(12x + 4)(12x + 4) = 42

Reorder the terms:
(4 + 12x)(12x + 4) = 42

Reorder the terms:
(4 + 12x)(4 + 12x) = 42

Multiply (4 + 12x) * (4 + 12x)
(4(4 + 12x) + 12x * (4 + 12x)) = 42
((4 * 4 + 12x * 4) + 12x * (4 + 12x)) = 42
((16 + 48x) + 12x * (4 + 12x)) = 42
(16 + 48x + (4 * 12x + 12x * 12x)) = 42
(16 + 48x + (48x + 144x2)) = 42

Combine like terms: 48x + 48x = 96x
(16 + 96x + 144x2) = 42

Solving
16 + 96x + 144x2 = 42

Solving for variable 'x'.

Reorder the terms:
16 + -42 + 96x + 144x2 = 42 + -42

Combine like terms: 16 + -42 = -26
-26 + 96x + 144x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-26 + 96x + 144x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + 48x + 72x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-13 + 48x + 72x2)' equal to zero and attempt to solve:

Simplifying
-13 + 48x + 72x2 = 0

Solving
-13 + 48x + 72x2 = 0

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

Divide each side by '72'.
-0.1805555556 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '0.1805555556' to each side of the equation.
-0.1805555556 + 0.6666666667x + 0.1805555556 + x2 = 0 + 0.1805555556

Reorder the terms:
-0.1805555556 + 0.1805555556 + 0.6666666667x + x2 = 0 + 0.1805555556

Combine like terms: -0.1805555556 + 0.1805555556 = 0.0000000000
0.0000000000 + 0.6666666667x + x2 = 0 + 0.1805555556
0.6666666667x + x2 = 0 + 0.1805555556

Combine like terms: 0 + 0.1805555556 = 0.1805555556
0.6666666667x + x2 = 0.1805555556

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 0.1805555556 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 0.1805555556 + 0.1111111112

Combine like terms: 0.1805555556 + 0.1111111112 = 0.2916666668
0.1111111112 + 0.6666666667x + x2 = 0.2916666668

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 0.2916666668

Calculate the square root of the right side: 0.540061725

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 0.540061725 and -0.540061725.

Subproblem 1
x + 0.3333333334 = 0.540061725

Simplifying
x + 0.3333333334 = 0.540061725

Reorder the terms:
0.3333333334 + x = 0.540061725

Solving
0.3333333334 + x = 0.540061725

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 0.540061725 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 0.540061725 + -0.3333333334
x = 0.540061725 + -0.3333333334

Combine like terms: 0.540061725 + -0.3333333334 = 0.2067283916
x = 0.2067283916

Simplifying
x = 0.2067283916

Subproblem 2
x + 0.3333333334 = -0.540061725

Simplifying
x + 0.3333333334 = -0.540061725

Reorder the terms:
0.3333333334 + x = -0.540061725

Solving
0.3333333334 + x = -0.540061725

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -0.540061725 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -0.540061725 + -0.3333333334
x = -0.540061725 + -0.3333333334

Combine like terms: -0.540061725 + -0.3333333334 = -0.8733950584
x = -0.8733950584

Simplifying
x = -0.8733950584

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2067283916, -0.8733950584}
Solution
x = {0.2067283916, -0.8733950584}