0=12x^2+38x+4

Solution for 0=12x^2+38x+4 equation:

Simplifying
0 = 12x2 + 38x + 4

Reorder the terms:
0 = 4 + 38x + 12x2

Solving
0 = 4 + 38x + 12x2

Solving for variable 'x'.

Combine like terms: 0 + -4 = -4
-4 + -38x + -12x2 = 4 + 38x + 12x2 + -4 + -38x + -12x2

Reorder the terms:
-4 + -38x + -12x2 = 4 + -4 + 38x + -38x + 12x2 + -12x2

Combine like terms: 4 + -4 = 0
-4 + -38x + -12x2 = 0 + 38x + -38x + 12x2 + -12x2
-4 + -38x + -12x2 = 38x + -38x + 12x2 + -12x2

Combine like terms: 38x + -38x = 0
-4 + -38x + -12x2 = 0 + 12x2 + -12x2
-4 + -38x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-4 + -38x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(2 + 19x + 6x2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(2 + 19x + 6x2)' equal to zero and attempt to solve:

Simplifying
2 + 19x + 6x2 = 0

Solving
2 + 19x + 6x2 = 0

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

Divide each side by '6'.
0.3333333333 + 3.166666667x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 3.166666667x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 3.166666667x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 3.166666667x + x2 = 0 + -0.3333333333
3.166666667x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
3.166666667x + x2 = -0.3333333333

The x term is 3.166666667x.  Take half its coefficient (1.583333334).
Square it (2.506944447) and add it to both sides.

Add '2.506944447' to each side of the equation.
3.166666667x + 2.506944447 + x2 = -0.3333333333 + 2.506944447

Reorder the terms:
2.506944447 + 3.166666667x + x2 = -0.3333333333 + 2.506944447

Combine like terms: -0.3333333333 + 2.506944447 = 2.1736111137
2.506944447 + 3.166666667x + x2 = 2.1736111137

Factor a perfect square on the left side:
(x + 1.583333334)(x + 1.583333334) = 2.1736111137

Calculate the square root of the right side: 1.474317169

Break this problem into two subproblems by setting 
(x + 1.583333334) equal to 1.474317169 and -1.474317169.

Subproblem 1
x + 1.583333334 = 1.474317169

Simplifying
x + 1.583333334 = 1.474317169

Reorder the terms:
1.583333334 + x = 1.474317169

Solving
1.583333334 + x = 1.474317169

Solving for variable 'x'.

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

Add '-1.583333334' to each side of the equation.
1.583333334 + -1.583333334 + x = 1.474317169 + -1.583333334

Combine like terms: 1.583333334 + -1.583333334 = 0.000000000
0.000000000 + x = 1.474317169 + -1.583333334
x = 1.474317169 + -1.583333334

Combine like terms: 1.474317169 + -1.583333334 = -0.109016165
x = -0.109016165

Simplifying
x = -0.109016165

Subproblem 2
x + 1.583333334 = -1.474317169

Simplifying
x + 1.583333334 = -1.474317169

Reorder the terms:
1.583333334 + x = -1.474317169

Solving
1.583333334 + x = -1.474317169

Solving for variable 'x'.

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

Add '-1.583333334' to each side of the equation.
1.583333334 + -1.583333334 + x = -1.474317169 + -1.583333334

Combine like terms: 1.583333334 + -1.583333334 = 0.000000000
0.000000000 + x = -1.474317169 + -1.583333334
x = -1.474317169 + -1.583333334

Combine like terms: -1.474317169 + -1.583333334 = -3.057650503
x = -3.057650503

Simplifying
x = -3.057650503

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.109016165, -3.057650503}
Solution
x = {-0.109016165, -3.057650503}