3(6+x)x=20

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Solution for 3(6+x)x=20 equation: 


Simplifying
3(6 + x) * x = 20

Reorder the terms for easier multiplication:
3x(6 + x) = 20
(6 * 3x + x * 3x) = 20
(18x + 3x2) = 20

Solving
18x + 3x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + 18x + 3x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 18x + 3x2 = 0

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

Divide each side by '3'.
-6.666666667 + 6x + x2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + 6x + 6.666666667 + x2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + 6x + x2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + 6x + x2 = 0 + 6.666666667
6x + x2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
6x + x2 = 6.666666667

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 6.666666667 + 9

Reorder the terms:
9 + 6x + x2 = 6.666666667 + 9

Combine like terms: 6.666666667 + 9 = 15.666666667
9 + 6x + x2 = 15.666666667

Factor a perfect square on the left side:
(x + 3)(x + 3) = 15.666666667

Calculate the square root of the right side: 3.958114029

Break this problem into two subproblems by setting 
(x + 3) equal to 3.958114029 and -3.958114029.


Subproblem 1
x + 3 = 3.958114029

Simplifying
x + 3 = 3.958114029

Reorder the terms:
3 + x = 3.958114029

Solving
3 + x = 3.958114029

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 3.958114029 + -3

Combine like terms: 3 + -3 = 0
0 + x = 3.958114029 + -3
x = 3.958114029 + -3

Combine like terms: 3.958114029 + -3 = 0.958114029
x = 0.958114029

Simplifying
x = 0.958114029


Subproblem 2
x + 3 = -3.958114029

Simplifying
x + 3 = -3.958114029

Reorder the terms:
3 + x = -3.958114029

Solving
3 + x = -3.958114029

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -3.958114029 + -3

Combine like terms: 3 + -3 = 0
0 + x = -3.958114029 + -3
x = -3.958114029 + -3

Combine like terms: -3.958114029 + -3 = -6.958114029
x = -6.958114029

Simplifying
x = -6.958114029


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.958114029, -6.958114029}

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