18=2(2x+4)2x

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Solution for 18=2(2x+4)2x equation: 


Simplifying
18 = 2(2x + 4) * 2x

Reorder the terms:
18 = 2(4 + 2x) * 2x

Reorder the terms for easier multiplication:
18 = 2 * 2x(4 + 2x)

Multiply 2 * 2
18 = 4x(4 + 2x)
18 = (4 * 4x + 2x * 4x)
18 = (16x + 8x2)

Solving
18 = 16x + 8x2

Solving for variable 'x'.

Reorder the terms:
18 + -16x + -8x2 = 16x + -16x + 8x2 + -8x2

Combine like terms: 16x + -16x = 0
18 + -16x + -8x2 = 0 + 8x2 + -8x2
18 + -16x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
18 + -16x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -8x + -4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(9 + -8x + -4x2)' equal to zero and attempt to solve:

Simplifying
9 + -8x + -4x2 = 0

Solving
9 + -8x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-2.25 + 2x + x2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + 2x + 2.25 + x2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + 2x + x2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + 2x + x2 = 0 + 2.25
2x + x2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
2x + x2 = 2.25

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 2.25 + 1

Reorder the terms:
1 + 2x + x2 = 2.25 + 1

Combine like terms: 2.25 + 1 = 3.25
1 + 2x + x2 = 3.25

Factor a perfect square on the left side:
(x + 1)(x + 1) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + 1) equal to 1.802775638 and -1.802775638.


Subproblem 1
x + 1 = 1.802775638

Simplifying
x + 1 = 1.802775638

Reorder the terms:
1 + x = 1.802775638

Solving
1 + x = 1.802775638

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 1.802775638 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.802775638 + -1
x = 1.802775638 + -1

Combine like terms: 1.802775638 + -1 = 0.802775638
x = 0.802775638

Simplifying
x = 0.802775638


Subproblem 2
x + 1 = -1.802775638

Simplifying
x + 1 = -1.802775638

Reorder the terms:
1 + x = -1.802775638

Solving
1 + x = -1.802775638

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -1.802775638 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.802775638 + -1
x = -1.802775638 + -1

Combine like terms: -1.802775638 + -1 = -2.802775638
x = -2.802775638

Simplifying
x = -2.802775638


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.802775638, -2.802775638}
Solution
x = {0.802775638, -2.802775638}

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