6x(x+10)=20

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Solution for 6x(x+10)=20 equation: 


Simplifying
6x(x + 10) = 20

Reorder the terms:
6x(10 + x) = 20
(10 * 6x + x * 6x) = 20
(60x + 6x2) = 20

Solving
60x + 6x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + 60x + 6x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 60x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 30x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-10 + 30x + 3x2)' equal to zero and attempt to solve:

Simplifying
-10 + 30x + 3x2 = 0

Solving
-10 + 30x + 3x2 = 0

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

Divide each side by '3'.
-3.333333333 + 10x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + 10x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + 10x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + 10x + x2 = 0 + 3.333333333
10x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
10x + x2 = 3.333333333

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 3.333333333 + 25

Reorder the terms:
25 + 10x + x2 = 3.333333333 + 25

Combine like terms: 3.333333333 + 25 = 28.333333333
25 + 10x + x2 = 28.333333333

Factor a perfect square on the left side:
(x + 5)(x + 5) = 28.333333333

Calculate the square root of the right side: 5.322906474

Break this problem into two subproblems by setting 
(x + 5) equal to 5.322906474 and -5.322906474.


Subproblem 1
x + 5 = 5.322906474

Simplifying
x + 5 = 5.322906474

Reorder the terms:
5 + x = 5.322906474

Solving
5 + x = 5.322906474

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 5.322906474 + -5

Combine like terms: 5 + -5 = 0
0 + x = 5.322906474 + -5
x = 5.322906474 + -5

Combine like terms: 5.322906474 + -5 = 0.322906474
x = 0.322906474

Simplifying
x = 0.322906474


Subproblem 2
x + 5 = -5.322906474

Simplifying
x + 5 = -5.322906474

Reorder the terms:
5 + x = -5.322906474

Solving
5 + x = -5.322906474

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -5.322906474 + -5

Combine like terms: 5 + -5 = 0
0 + x = -5.322906474 + -5
x = -5.322906474 + -5

Combine like terms: -5.322906474 + -5 = -10.322906474
x = -10.322906474

Simplifying
x = -10.322906474


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.322906474, -10.322906474}
Solution
x = {0.322906474, -10.322906474}

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