6(4x-1)(4x+1)=x

Solution for 6(4x-1)(4x+1)=x equation:

Simplifying
6(4x + -1)(4x + 1) = x

Reorder the terms:
6(-1 + 4x)(4x + 1) = x

Reorder the terms:
6(-1 + 4x)(1 + 4x) = x

Multiply (-1 + 4x) * (1 + 4x)
6(-1(1 + 4x) + 4x * (1 + 4x)) = x
6((1 * -1 + 4x * -1) + 4x * (1 + 4x)) = x
6((-1 + -4x) + 4x * (1 + 4x)) = x
6(-1 + -4x + (1 * 4x + 4x * 4x)) = x
6(-1 + -4x + (4x + 16x2)) = x

Combine like terms: -4x + 4x = 0
6(-1 + 0 + 16x2) = x
6(-1 + 16x2) = x
(-1 * 6 + 16x2 * 6) = x
(-6 + 96x2) = x

Solving
-6 + 96x2 = x

Solving for variable 'x'.

Reorder the terms:
-6 + -1x + 96x2 = x + -1x

Combine like terms: x + -1x = 0
-6 + -1x + 96x2 = 0

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

Divide each side by '96'.
-0.0625 + -0.01041666667x + x2 = 0

Move the constant term to the right:

Add '0.0625' to each side of the equation.
-0.0625 + -0.01041666667x + 0.0625 + x2 = 0 + 0.0625

Reorder the terms:
-0.0625 + 0.0625 + -0.01041666667x + x2 = 0 + 0.0625

Combine like terms: -0.0625 + 0.0625 = 0.0000
0.0000 + -0.01041666667x + x2 = 0 + 0.0625
-0.01041666667x + x2 = 0 + 0.0625

Combine like terms: 0 + 0.0625 = 0.0625
-0.01041666667x + x2 = 0.0625

The x term is -0.01041666667x.  Take half its coefficient (-0.005208333335).
Square it (0.00002712673613) and add it to both sides.

Add '0.00002712673613' to each side of the equation.
-0.01041666667x + 0.00002712673613 + x2 = 0.0625 + 0.00002712673613

Reorder the terms:
0.00002712673613 + -0.01041666667x + x2 = 0.0625 + 0.00002712673613

Combine like terms: 0.0625 + 0.00002712673613 = 0.06252712673613
0.00002712673613 + -0.01041666667x + x2 = 0.06252712673613

Factor a perfect square on the left side:
(x + -0.005208333335)(x + -0.005208333335) = 0.06252712673613

Calculate the square root of the right side: 0.250054248

Break this problem into two subproblems by setting 
(x + -0.005208333335) equal to 0.250054248 and -0.250054248.

Subproblem 1
x + -0.005208333335 = 0.250054248

Simplifying
x + -0.005208333335 = 0.250054248

Reorder the terms:
-0.005208333335 + x = 0.250054248

Solving
-0.005208333335 + x = 0.250054248

Solving for variable 'x'.

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

Add '0.005208333335' to each side of the equation.
-0.005208333335 + 0.005208333335 + x = 0.250054248 + 0.005208333335

Combine like terms: -0.005208333335 + 0.005208333335 = 0.000000000000
0.000000000000 + x = 0.250054248 + 0.005208333335
x = 0.250054248 + 0.005208333335

Combine like terms: 0.250054248 + 0.005208333335 = 0.255262581335
x = 0.255262581335

Simplifying
x = 0.255262581335

Subproblem 2
x + -0.005208333335 = -0.250054248

Simplifying
x + -0.005208333335 = -0.250054248

Reorder the terms:
-0.005208333335 + x = -0.250054248

Solving
-0.005208333335 + x = -0.250054248

Solving for variable 'x'.

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

Add '0.005208333335' to each side of the equation.
-0.005208333335 + 0.005208333335 + x = -0.250054248 + 0.005208333335

Combine like terms: -0.005208333335 + 0.005208333335 = 0.000000000000
0.000000000000 + x = -0.250054248 + 0.005208333335
x = -0.250054248 + 0.005208333335

Combine like terms: -0.250054248 + 0.005208333335 = -0.244845914665
x = -0.244845914665

Simplifying
x = -0.244845914665

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.255262581335, -0.244845914665}