2x(2+4x)=18

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

Simplifying
2x(2 + 4x) = 18
(2 * 2x + 4x * 2x) = 18
(4x + 8x2) = 18

Solving
4x + 8x2 = 18

Solving for variable 'x'.

Reorder the terms:
-18 + 4x + 8x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 4x + 8x2 = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + 2x + 4x2)' equal to zero and attempt to solve:

Simplifying
-9 + 2x + 4x2 = 0

Solving
-9 + 2x + 4x2 = 0

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

Divide each side by '4'.
-2.25 + 0.5x + x2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + 0.5x + 2.25 + x2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + 0.5x + x2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + 0.5x + x2 = 0 + 2.25
0.5x + x2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
0.5x + x2 = 2.25

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 2.25 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 2.25 + 0.0625

Combine like terms: 2.25 + 0.0625 = 2.3125
0.0625 + 0.5x + x2 = 2.3125

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 2.3125

Calculate the square root of the right side: 1.520690633

Break this problem into two subproblems by setting 
(x + 0.25) equal to 1.520690633 and -1.520690633.

Subproblem 1
x + 0.25 = 1.520690633

Simplifying
x + 0.25 = 1.520690633

Reorder the terms:
0.25 + x = 1.520690633

Solving
0.25 + x = 1.520690633

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 1.520690633 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 1.520690633 + -0.25
x = 1.520690633 + -0.25

Combine like terms: 1.520690633 + -0.25 = 1.270690633
x = 1.270690633

Simplifying
x = 1.270690633

Subproblem 2
x + 0.25 = -1.520690633

Simplifying
x + 0.25 = -1.520690633

Reorder the terms:
0.25 + x = -1.520690633

Solving
0.25 + x = -1.520690633

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -1.520690633 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -1.520690633 + -0.25
x = -1.520690633 + -0.25

Combine like terms: -1.520690633 + -0.25 = -1.770690633
x = -1.770690633

Simplifying
x = -1.770690633

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.270690633, -1.770690633}
Solution
x = {1.270690633, -1.770690633}