9x(x+4)=6

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Solution for 9x(x+4)=6 equation: 


Simplifying
9x(x + 4) = 6

Reorder the terms:
9x(4 + x) = 6
(4 * 9x + x * 9x) = 6
(36x + 9x2) = 6

Solving
36x + 9x2 = 6

Solving for variable 'x'.

Reorder the terms:
-6 + 36x + 9x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 36x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 12x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-2 + 12x + 3x2)' equal to zero and attempt to solve:

Simplifying
-2 + 12x + 3x2 = 0

Solving
-2 + 12x + 3x2 = 0

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

Divide each side by '3'.
-0.6666666667 + 4x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 4x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 4x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 4x + x2 = 0 + 0.6666666667
4x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
4x + x2 = 0.6666666667

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 0.6666666667 + 4

Reorder the terms:
4 + 4x + x2 = 0.6666666667 + 4

Combine like terms: 0.6666666667 + 4 = 4.6666666667
4 + 4x + x2 = 4.6666666667

Factor a perfect square on the left side:
(x + 2)(x + 2) = 4.6666666667

Calculate the square root of the right side: 2.160246899

Break this problem into two subproblems by setting 
(x + 2) equal to 2.160246899 and -2.160246899.


Subproblem 1
x + 2 = 2.160246899

Simplifying
x + 2 = 2.160246899

Reorder the terms:
2 + x = 2.160246899

Solving
2 + x = 2.160246899

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 2.160246899 + -2

Combine like terms: 2 + -2 = 0
0 + x = 2.160246899 + -2
x = 2.160246899 + -2

Combine like terms: 2.160246899 + -2 = 0.160246899
x = 0.160246899

Simplifying
x = 0.160246899


Subproblem 2
x + 2 = -2.160246899

Simplifying
x + 2 = -2.160246899

Reorder the terms:
2 + x = -2.160246899

Solving
2 + x = -2.160246899

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -2.160246899 + -2

Combine like terms: 2 + -2 = 0
0 + x = -2.160246899 + -2
x = -2.160246899 + -2

Combine like terms: -2.160246899 + -2 = -4.160246899
x = -4.160246899

Simplifying
x = -4.160246899


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.160246899, -4.160246899}
Solution
x = {0.160246899, -4.160246899}

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