(1-4x)2-(2x)(x+2)=

Solution for (1-4x)2-(2x)(x+2)= equation:

Simplifying
(1 + -4x) * 2 + -1(2x)(x + 2) = 0

Reorder the terms for easier multiplication:
2(1 + -4x) + -1(2x)(x + 2) = 0
(1 * 2 + -4x * 2) + -1(2x)(x + 2) = 0
(2 + -8x) + -1(2x)(x + 2) = 0

Remove parenthesis around (2x)
2 + -8x + -1 * 2x(x + 2) = 0

Reorder the terms:
2 + -8x + -1 * 2x(2 + x) = 0

Multiply -1 * 2
2 + -8x + -2x(2 + x) = 0
2 + -8x + (2 * -2x + x * -2x) = 0
2 + -8x + (-4x + -2x2) = 0

Combine like terms: -8x + -4x = -12x
2 + -12x + -2x2 = 0

Solving
2 + -12x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -6x + -1x2) = 0

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

Simplifying
1 + -6x + -1x2 = 0

Solving
1 + -6x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + 6x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 6x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 6x + x2 = 0 + 1

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

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

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 1 + 9

Reorder the terms:
9 + 6x + x2 = 1 + 9

Combine like terms: 1 + 9 = 10
9 + 6x + x2 = 10

Factor a perfect square on the left side:
(x + 3)(x + 3) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + 3) equal to 3.16227766 and -3.16227766.

Subproblem 1
x + 3 = 3.16227766

Simplifying
x + 3 = 3.16227766

Reorder the terms:
3 + x = 3.16227766

Solving
3 + x = 3.16227766

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 3.16227766 + -3

Combine like terms: 3 + -3 = 0
0 + x = 3.16227766 + -3
x = 3.16227766 + -3

Combine like terms: 3.16227766 + -3 = 0.16227766
x = 0.16227766

Simplifying
x = 0.16227766

Subproblem 2
x + 3 = -3.16227766

Simplifying
x + 3 = -3.16227766

Reorder the terms:
3 + x = -3.16227766

Solving
3 + x = -3.16227766

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -3.16227766 + -3

Combine like terms: 3 + -3 = 0
0 + x = -3.16227766 + -3
x = -3.16227766 + -3

Combine like terms: -3.16227766 + -3 = -6.16227766
x = -6.16227766

Simplifying
x = -6.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.16227766, -6.16227766}
Solution
x = {0.16227766, -6.16227766}