6(x^2+20x+100)=20

Solution for 6(x^2+20x+100)=20 equation:

Simplifying
6(x2 + 20x + 100) = 20

Reorder the terms:
6(100 + 20x + x2) = 20
(100 * 6 + 20x * 6 + x2 * 6) = 20
(600 + 120x + 6x2) = 20

Solving
600 + 120x + 6x2 = 20

Solving for variable 'x'.

Reorder the terms:
600 + -20 + 120x + 6x2 = 20 + -20

Combine like terms: 600 + -20 = 580
580 + 120x + 6x2 = 20 + -20

Combine like terms: 20 + -20 = 0
580 + 120x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(290 + 60x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(290 + 60x + 3x2)' equal to zero and attempt to solve:

Simplifying
290 + 60x + 3x2 = 0

Solving
290 + 60x + 3x2 = 0

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

Divide each side by '3'.
96.66666667 + 20x + x2 = 0

Move the constant term to the right:

Add '-96.66666667' to each side of the equation.
96.66666667 + 20x + -96.66666667 + x2 = 0 + -96.66666667

Reorder the terms:
96.66666667 + -96.66666667 + 20x + x2 = 0 + -96.66666667

Combine like terms: 96.66666667 + -96.66666667 = 0.00000000
0.00000000 + 20x + x2 = 0 + -96.66666667
20x + x2 = 0 + -96.66666667

Combine like terms: 0 + -96.66666667 = -96.66666667
20x + x2 = -96.66666667

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = -96.66666667 + 100

Reorder the terms:
100 + 20x + x2 = -96.66666667 + 100

Combine like terms: -96.66666667 + 100 = 3.33333333
100 + 20x + x2 = 3.33333333

Factor a perfect square on the left side:
(x + 10)(x + 10) = 3.33333333

Calculate the square root of the right side: 1.825741857

Break this problem into two subproblems by setting 
(x + 10) equal to 1.825741857 and -1.825741857.

Subproblem 1
x + 10 = 1.825741857

Simplifying
x + 10 = 1.825741857

Reorder the terms:
10 + x = 1.825741857

Solving
10 + x = 1.825741857

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 1.825741857 + -10

Combine like terms: 10 + -10 = 0
0 + x = 1.825741857 + -10
x = 1.825741857 + -10

Combine like terms: 1.825741857 + -10 = -8.174258143
x = -8.174258143

Simplifying
x = -8.174258143

Subproblem 2
x + 10 = -1.825741857

Simplifying
x + 10 = -1.825741857

Reorder the terms:
10 + x = -1.825741857

Solving
10 + x = -1.825741857

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -1.825741857 + -10

Combine like terms: 10 + -10 = 0
0 + x = -1.825741857 + -10
x = -1.825741857 + -10

Combine like terms: -1.825741857 + -10 = -11.825741857
x = -11.825741857

Simplifying
x = -11.825741857

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-8.174258143, -11.825741857}
Solution
x = {-8.174258143, -11.825741857}