4x[3(x-12)+1]=10

Solution for 4x[3(x-12)+1]=10 equation:

Simplifying
4x[3(x + -12) + 1] = 10

Reorder the terms:
4x[3(-12 + x) + 1] = 10
4x[(-12 * 3 + x * 3) + 1] = 10
4x[(-36 + 3x) + 1] = 10

Reorder the terms:
4x[-36 + 1 + 3x] = 10

Combine like terms: -36 + 1 = -35
4x[-35 + 3x] = 10
[-35 * 4x + 3x * 4x] = 10
[-140x + 12x2] = 10

Solving
-140x + 12x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + -140x + 12x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -140x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -70x + 6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -70x + 6x2)' equal to zero and attempt to solve:

Simplifying
-5 + -70x + 6x2 = 0

Solving
-5 + -70x + 6x2 = 0

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

Divide each side by '6'.
-0.8333333333 + -11.66666667x + x2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -11.66666667x + 0.8333333333 + x2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -11.66666667x + x2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -11.66666667x + x2 = 0 + 0.8333333333
-11.66666667x + x2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-11.66666667x + x2 = 0.8333333333

The x term is -11.66666667x.  Take half its coefficient (-5.833333335).
Square it (34.02777780) and add it to both sides.

Add '34.02777780' to each side of the equation.
-11.66666667x + 34.02777780 + x2 = 0.8333333333 + 34.02777780

Reorder the terms:
34.02777780 + -11.66666667x + x2 = 0.8333333333 + 34.02777780

Combine like terms: 0.8333333333 + 34.02777780 = 34.8611111333
34.02777780 + -11.66666667x + x2 = 34.8611111333

Factor a perfect square on the left side:
(x + -5.833333335)(x + -5.833333335) = 34.8611111333

Calculate the square root of the right side: 5.904329863

Break this problem into two subproblems by setting 
(x + -5.833333335) equal to 5.904329863 and -5.904329863.

Subproblem 1
x + -5.833333335 = 5.904329863

Simplifying
x + -5.833333335 = 5.904329863

Reorder the terms:
-5.833333335 + x = 5.904329863

Solving
-5.833333335 + x = 5.904329863

Solving for variable 'x'.

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

Add '5.833333335' to each side of the equation.
-5.833333335 + 5.833333335 + x = 5.904329863 + 5.833333335

Combine like terms: -5.833333335 + 5.833333335 = 0.000000000
0.000000000 + x = 5.904329863 + 5.833333335
x = 5.904329863 + 5.833333335

Combine like terms: 5.904329863 + 5.833333335 = 11.737663198
x = 11.737663198

Simplifying
x = 11.737663198

Subproblem 2
x + -5.833333335 = -5.904329863

Simplifying
x + -5.833333335 = -5.904329863

Reorder the terms:
-5.833333335 + x = -5.904329863

Solving
-5.833333335 + x = -5.904329863

Solving for variable 'x'.

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

Add '5.833333335' to each side of the equation.
-5.833333335 + 5.833333335 + x = -5.904329863 + 5.833333335

Combine like terms: -5.833333335 + 5.833333335 = 0.000000000
0.000000000 + x = -5.904329863 + 5.833333335
x = -5.904329863 + 5.833333335

Combine like terms: -5.904329863 + 5.833333335 = -0.070996528
x = -0.070996528

Simplifying
x = -0.070996528

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.737663198, -0.070996528}
Solution
x = {11.737663198, -0.070996528}