4x(4x)+2x-6=0

Solution for 4x(4x)+2x-6=0 equation:

Simplifying
4x(4x) + 2x + -6 = 0

Remove parenthesis around (4x)
4x * 4x + 2x + -6 = 0

Reorder the terms for easier multiplication:
4 * 4x * x + 2x + -6 = 0

Multiply 4 * 4
16x * x + 2x + -6 = 0

Multiply x * x
16x2 + 2x + -6 = 0

Reorder the terms:
-6 + 2x + 16x2 = 0

Solving
-6 + 2x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + x + 8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + x + 8x2)' equal to zero and attempt to solve:

Simplifying
-3 + x + 8x2 = 0

Solving
-3 + x + 8x2 = 0

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

Divide each side by '8'.
-0.375 + 0.125x + x2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + 0.125x + 0.375 + x2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + 0.125x + x2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + 0.125x + x2 = 0 + 0.375
0.125x + x2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
0.125x + x2 = 0.375

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.125x + 0.25 + x2 = 0.375 + 0.25

Reorder the terms:
0.25 + 0.125x + x2 = 0.375 + 0.25

Combine like terms: 0.375 + 0.25 = 0.625
0.25 + 0.125x + x2 = 0.625

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.625

Calculate the square root of the right side: 0.790569415

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.790569415 and -0.790569415.

Subproblem 1
x + 0.5 = 0.790569415

Simplifying
x + 0.5 = 0.790569415

Reorder the terms:
0.5 + x = 0.790569415

Solving
0.5 + x = 0.790569415

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0.790569415 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.790569415 + -0.5
x = 0.790569415 + -0.5

Combine like terms: 0.790569415 + -0.5 = 0.290569415
x = 0.290569415

Simplifying
x = 0.290569415

Subproblem 2
x + 0.5 = -0.790569415

Simplifying
x + 0.5 = -0.790569415

Reorder the terms:
0.5 + x = -0.790569415

Solving
0.5 + x = -0.790569415

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -0.790569415 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.790569415 + -0.5
x = -0.790569415 + -0.5

Combine like terms: -0.790569415 + -0.5 = -1.290569415
x = -1.290569415

Simplifying
x = -1.290569415

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.290569415, -1.290569415}
Solution
x = {0.290569415, -1.290569415}