(x-4)(x)(9)=138

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Solution for (x-4)(x)(9)=138 equation: 


Simplifying
(x + -4)(x)(9) = 138

Reorder the terms:
(-4 + x)(x)(9) = 138

Reorder the terms for easier multiplication:
9x(-4 + x) = 138
(-4 * 9x + x * 9x) = 138
(-36x + 9x2) = 138

Solving
-36x + 9x2 = 138

Solving for variable 'x'.

Reorder the terms:
-138 + -36x + 9x2 = 138 + -138

Combine like terms: 138 + -138 = 0
-138 + -36x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-46 + -12x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-46 + -12x + 3x2)' equal to zero and attempt to solve:

Simplifying
-46 + -12x + 3x2 = 0

Solving
-46 + -12x + 3x2 = 0

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

Divide each side by '3'.
-15.33333333 + -4x + x2 = 0

Move the constant term to the right:

Add '15.33333333' to each side of the equation.
-15.33333333 + -4x + 15.33333333 + x2 = 0 + 15.33333333

Reorder the terms:
-15.33333333 + 15.33333333 + -4x + x2 = 0 + 15.33333333

Combine like terms: -15.33333333 + 15.33333333 = 0.00000000
0.00000000 + -4x + x2 = 0 + 15.33333333
-4x + x2 = 0 + 15.33333333

Combine like terms: 0 + 15.33333333 = 15.33333333
-4x + x2 = 15.33333333

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 = 15.33333333 + 4

Reorder the terms:
4 + -4x + x2 = 15.33333333 + 4

Combine like terms: 15.33333333 + 4 = 19.33333333
4 + -4x + x2 = 19.33333333

Factor a perfect square on the left side:
(x + -2)(x + -2) = 19.33333333

Calculate the square root of the right side: 4.396968652

Break this problem into two subproblems by setting 
(x + -2) equal to 4.396968652 and -4.396968652.


Subproblem 1
x + -2 = 4.396968652

Simplifying
x + -2 = 4.396968652

Reorder the terms:
-2 + x = 4.396968652

Solving
-2 + x = 4.396968652

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 = 4.396968652 + 2

Combine like terms: -2 + 2 = 0
0 + x = 4.396968652 + 2
x = 4.396968652 + 2

Combine like terms: 4.396968652 + 2 = 6.396968652
x = 6.396968652

Simplifying
x = 6.396968652


Subproblem 2
x + -2 = -4.396968652

Simplifying
x + -2 = -4.396968652

Reorder the terms:
-2 + x = -4.396968652

Solving
-2 + x = -4.396968652

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 = -4.396968652 + 2

Combine like terms: -2 + 2 = 0
0 + x = -4.396968652 + 2
x = -4.396968652 + 2

Combine like terms: -4.396968652 + 2 = -2.396968652
x = -2.396968652

Simplifying
x = -2.396968652


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.396968652, -2.396968652}
Solution
x = {6.396968652, -2.396968652}

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