x=4(4x-1)(4x-1)

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

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

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

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

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

Combine like terms: -4x + -4x = -8x
x = 4(1 + -8x + 16x2)
x = (1 * 4 + -8x * 4 + 16x2 * 4)
x = (4 + -32x + 64x2)

Solving
x = 4 + -32x + 64x2

Solving for variable 'x'.

Reorder the terms:
-4 + x + 32x + -64x2 = 4 + -32x + 64x2 + -4 + 32x + -64x2

Combine like terms: x + 32x = 33x
-4 + 33x + -64x2 = 4 + -32x + 64x2 + -4 + 32x + -64x2

Reorder the terms:
-4 + 33x + -64x2 = 4 + -4 + -32x + 32x + 64x2 + -64x2

Combine like terms: 4 + -4 = 0
-4 + 33x + -64x2 = 0 + -32x + 32x + 64x2 + -64x2
-4 + 33x + -64x2 = -32x + 32x + 64x2 + -64x2

Combine like terms: -32x + 32x = 0
-4 + 33x + -64x2 = 0 + 64x2 + -64x2
-4 + 33x + -64x2 = 64x2 + -64x2

Combine like terms: 64x2 + -64x2 = 0
-4 + 33x + -64x2 = 0

Begin completing the square.  Divide all terms by
-64 the coefficient of the squared term: 

Divide each side by '-64'.
0.0625 + -0.515625x + x2 = 0

Move the constant term to the right:

Add '-0.0625' to each side of the equation.
0.0625 + -0.515625x + -0.0625 + x2 = 0 + -0.0625

Reorder the terms:
0.0625 + -0.0625 + -0.515625x + x2 = 0 + -0.0625

Combine like terms: 0.0625 + -0.0625 = 0.0000
0.0000 + -0.515625x + x2 = 0 + -0.0625
-0.515625x + x2 = 0 + -0.0625

Combine like terms: 0 + -0.0625 = -0.0625
-0.515625x + x2 = -0.0625

The x term is -0.515625x.  Take half its coefficient (-0.2578125).
Square it (0.06646728516) and add it to both sides.

Add '0.06646728516' to each side of the equation.
-0.515625x + 0.06646728516 + x2 = -0.0625 + 0.06646728516

Reorder the terms:
0.06646728516 + -0.515625x + x2 = -0.0625 + 0.06646728516

Combine like terms: -0.0625 + 0.06646728516 = 0.00396728516
0.06646728516 + -0.515625x + x2 = 0.00396728516

Factor a perfect square on the left side:
(x + -0.2578125)(x + -0.2578125) = 0.00396728516

Calculate the square root of the right side: 0.062986389

Break this problem into two subproblems by setting 
(x + -0.2578125) equal to 0.062986389 and -0.062986389.

Subproblem 1
x + -0.2578125 = 0.062986389

Simplifying
x + -0.2578125 = 0.062986389

Reorder the terms:
-0.2578125 + x = 0.062986389

Solving
-0.2578125 + x = 0.062986389

Solving for variable 'x'.

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

Add '0.2578125' to each side of the equation.
-0.2578125 + 0.2578125 + x = 0.062986389 + 0.2578125

Combine like terms: -0.2578125 + 0.2578125 = 0.0000000
0.0000000 + x = 0.062986389 + 0.2578125
x = 0.062986389 + 0.2578125

Combine like terms: 0.062986389 + 0.2578125 = 0.320798889
x = 0.320798889

Simplifying
x = 0.320798889

Subproblem 2
x + -0.2578125 = -0.062986389

Simplifying
x + -0.2578125 = -0.062986389

Reorder the terms:
-0.2578125 + x = -0.062986389

Solving
-0.2578125 + x = -0.062986389

Solving for variable 'x'.

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

Add '0.2578125' to each side of the equation.
-0.2578125 + 0.2578125 + x = -0.062986389 + 0.2578125

Combine like terms: -0.2578125 + 0.2578125 = 0.0000000
0.0000000 + x = -0.062986389 + 0.2578125
x = -0.062986389 + 0.2578125

Combine like terms: -0.062986389 + 0.2578125 = 0.194826111
x = 0.194826111

Simplifying
x = 0.194826111

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.320798889, 0.194826111}