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

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

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

Reorder the terms:
4 * 1(2 + x)(2x + 2) = x

Reorder the terms:
4 * 1(2 + x)(2 + 2x) = x

Multiply 4 * 1
4(2 + x)(2 + 2x) = x

Multiply (2 + x) * (2 + 2x)
4(2(2 + 2x) + x(2 + 2x)) = x
4((2 * 2 + 2x * 2) + x(2 + 2x)) = x
4((4 + 4x) + x(2 + 2x)) = x
4(4 + 4x + (2 * x + 2x * x)) = x
4(4 + 4x + (2x + 2x2)) = x

Combine like terms: 4x + 2x = 6x
4(4 + 6x + 2x2) = x
(4 * 4 + 6x * 4 + 2x2 * 4) = x
(16 + 24x + 8x2) = x

Solving
16 + 24x + 8x2 = x

Solving for variable 'x'.

Reorder the terms:
16 + 24x + -1x + 8x2 = x + -1x

Combine like terms: 24x + -1x = 23x
16 + 23x + 8x2 = x + -1x

Combine like terms: x + -1x = 0
16 + 23x + 8x2 = 0

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

Divide each side by '8'.
2 + 2.875x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 2.875x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 2.875x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 2.875x + x2 = 0 + -2
2.875x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
2.875x + x2 = -2

The x term is 2.875x.  Take half its coefficient (1.4375).
Square it (2.06640625) and add it to both sides.

Add '2.06640625' to each side of the equation.
2.875x + 2.06640625 + x2 = -2 + 2.06640625

Reorder the terms:
2.06640625 + 2.875x + x2 = -2 + 2.06640625

Combine like terms: -2 + 2.06640625 = 0.06640625
2.06640625 + 2.875x + x2 = 0.06640625

Factor a perfect square on the left side:
(x + 1.4375)(x + 1.4375) = 0.06640625

Calculate the square root of the right side: 0.257694102

Break this problem into two subproblems by setting 
(x + 1.4375) equal to 0.257694102 and -0.257694102.

Subproblem 1
x + 1.4375 = 0.257694102

Simplifying
x + 1.4375 = 0.257694102

Reorder the terms:
1.4375 + x = 0.257694102

Solving
1.4375 + x = 0.257694102

Solving for variable 'x'.

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

Add '-1.4375' to each side of the equation.
1.4375 + -1.4375 + x = 0.257694102 + -1.4375

Combine like terms: 1.4375 + -1.4375 = 0.0000
0.0000 + x = 0.257694102 + -1.4375
x = 0.257694102 + -1.4375

Combine like terms: 0.257694102 + -1.4375 = -1.179805898
x = -1.179805898

Simplifying
x = -1.179805898

Subproblem 2
x + 1.4375 = -0.257694102

Simplifying
x + 1.4375 = -0.257694102

Reorder the terms:
1.4375 + x = -0.257694102

Solving
1.4375 + x = -0.257694102

Solving for variable 'x'.

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

Add '-1.4375' to each side of the equation.
1.4375 + -1.4375 + x = -0.257694102 + -1.4375

Combine like terms: 1.4375 + -1.4375 = 0.0000
0.0000 + x = -0.257694102 + -1.4375
x = -0.257694102 + -1.4375

Combine like terms: -0.257694102 + -1.4375 = -1.695194102
x = -1.695194102

Simplifying
x = -1.695194102

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.179805898, -1.695194102}