2x(x+6)=40

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Solution for 2x(x+6)=40 equation: 


Simplifying
2x(x + 6) = 40

Reorder the terms:
2x(6 + x) = 40
(6 * 2x + x * 2x) = 40
(12x + 2x2) = 40

Solving
12x + 2x2 = 40

Solving for variable 'x'.

Reorder the terms:
-40 + 12x + 2x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + 6x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-20 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
-20 + 6x + x2 = 0

Solving
-20 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 6x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 6x + x2 = 0 + 20

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

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

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 = 20 + 9

Reorder the terms:
9 + 6x + x2 = 20 + 9

Combine like terms: 20 + 9 = 29
9 + 6x + x2 = 29

Factor a perfect square on the left side:
(x + 3)(x + 3) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(x + 3) equal to 5.385164807 and -5.385164807.


Subproblem 1
x + 3 = 5.385164807

Simplifying
x + 3 = 5.385164807

Reorder the terms:
3 + x = 5.385164807

Solving
3 + x = 5.385164807

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 = 5.385164807 + -3

Combine like terms: 3 + -3 = 0
0 + x = 5.385164807 + -3
x = 5.385164807 + -3

Combine like terms: 5.385164807 + -3 = 2.385164807
x = 2.385164807

Simplifying
x = 2.385164807


Subproblem 2
x + 3 = -5.385164807

Simplifying
x + 3 = -5.385164807

Reorder the terms:
3 + x = -5.385164807

Solving
3 + x = -5.385164807

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 = -5.385164807 + -3

Combine like terms: 3 + -3 = 0
0 + x = -5.385164807 + -3
x = -5.385164807 + -3

Combine like terms: -5.385164807 + -3 = -8.385164807
x = -8.385164807

Simplifying
x = -8.385164807


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.385164807, -8.385164807}
Solution
x = {2.385164807, -8.385164807}

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