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

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


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

Reorder the terms:
2(2 + 4x) = 4x(x + -1)
(2 * 2 + 4x * 2) = 4x(x + -1)
(4 + 8x) = 4x(x + -1)

Reorder the terms:
4 + 8x = 4x(-1 + x)
4 + 8x = (-1 * 4x + x * 4x)
4 + 8x = (-4x + 4x2)

Solving
4 + 8x = -4x + 4x2

Solving for variable 'x'.

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

Reorder the terms:
4 + 12x + -4x2 = -4x + 4x + 4x2 + -4x2

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

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

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 3x + -1x2) = 0

Ignore the factor 4.

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

Simplifying
1 + 3x + -1x2 = 0

Solving
1 + 3x + -1x2 = 0

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

Divide each side by '-1'.
-1 + -3x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -3x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -3x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x + x2 = 0 + 1
-3x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-3x + x2 = 1

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 1 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 1 + 2.25

Combine like terms: 1 + 2.25 = 3.25
2.25 + -3x + x2 = 3.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.802775638 and -1.802775638.


Subproblem 1
x + -1.5 = 1.802775638

Simplifying
x + -1.5 = 1.802775638

Reorder the terms:
-1.5 + x = 1.802775638

Solving
-1.5 + x = 1.802775638

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 1.802775638 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 1.802775638 + 1.5
x = 1.802775638 + 1.5

Combine like terms: 1.802775638 + 1.5 = 3.302775638
x = 3.302775638

Simplifying
x = 3.302775638


Subproblem 2
x + -1.5 = -1.802775638

Simplifying
x + -1.5 = -1.802775638

Reorder the terms:
-1.5 + x = -1.802775638

Solving
-1.5 + x = -1.802775638

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -1.802775638 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -1.802775638 + 1.5
x = -1.802775638 + 1.5

Combine like terms: -1.802775638 + 1.5 = -0.302775638
x = -0.302775638

Simplifying
x = -0.302775638


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.302775638, -0.302775638}
Solution
x = {3.302775638, -0.302775638}

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