2x(4+3x)=9

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Solution for 2x(4+3x)=9 equation: 


Simplifying
2x(4 + 3x) = 9
(4 * 2x + 3x * 2x) = 9
(8x + 6x2) = 9

Solving
8x + 6x2 = 9

Solving for variable 'x'.

Reorder the terms:
-9 + 8x + 6x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 8x + 6x2 = 0

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

Divide each side by '6'.
-1.5 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 1.333333333x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 1.333333333x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 1.333333333x + x2 = 0 + 1.5
1.333333333x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
1.333333333x + x2 = 1.5

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = 1.5 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 1.5 + 0.4444444442

Combine like terms: 1.5 + 0.4444444442 = 1.9444444442
0.4444444442 + 1.333333333x + x2 = 1.9444444442

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 1.9444444442

Calculate the square root of the right side: 1.394433377

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 1.394433377 and -1.394433377.


Subproblem 1
x + 0.6666666665 = 1.394433377

Simplifying
x + 0.6666666665 = 1.394433377

Reorder the terms:
0.6666666665 + x = 1.394433377

Solving
0.6666666665 + x = 1.394433377

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = 1.394433377 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = 1.394433377 + -0.6666666665
x = 1.394433377 + -0.6666666665

Combine like terms: 1.394433377 + -0.6666666665 = 0.7277667105
x = 0.7277667105

Simplifying
x = 0.7277667105


Subproblem 2
x + 0.6666666665 = -1.394433377

Simplifying
x + 0.6666666665 = -1.394433377

Reorder the terms:
0.6666666665 + x = -1.394433377

Solving
0.6666666665 + x = -1.394433377

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = -1.394433377 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = -1.394433377 + -0.6666666665
x = -1.394433377 + -0.6666666665

Combine like terms: -1.394433377 + -0.6666666665 = -2.0611000435
x = -2.0611000435

Simplifying
x = -2.0611000435


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7277667105, -2.0611000435}

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