x(x+6)*2=60

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Solution for x(x+6)*2=60 equation: 


Simplifying
x(x + 6) * 2 = 60

Reorder the terms:
x(6 + x) * 2 = 60

Reorder the terms for easier multiplication:
2x(6 + x) = 60
(6 * 2x + x * 2x) = 60
(12x + 2x2) = 60

Solving
12x + 2x2 = 60

Solving for variable 'x'.

Reorder the terms:
-60 + 12x + 2x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + 6x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-30 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
-30 + 6x + x2 = 0

Solving
-30 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 6x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 6x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 6x + x2 = 0 + 30
6x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
6x + x2 = 30

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 = 30 + 9

Reorder the terms:
9 + 6x + x2 = 30 + 9

Combine like terms: 30 + 9 = 39
9 + 6x + x2 = 39

Factor a perfect square on the left side:
(x + 3)(x + 3) = 39

Calculate the square root of the right side: 6.244997998

Break this problem into two subproblems by setting 
(x + 3) equal to 6.244997998 and -6.244997998.


Subproblem 1
x + 3 = 6.244997998

Simplifying
x + 3 = 6.244997998

Reorder the terms:
3 + x = 6.244997998

Solving
3 + x = 6.244997998

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 = 6.244997998 + -3

Combine like terms: 3 + -3 = 0
0 + x = 6.244997998 + -3
x = 6.244997998 + -3

Combine like terms: 6.244997998 + -3 = 3.244997998
x = 3.244997998

Simplifying
x = 3.244997998


Subproblem 2
x + 3 = -6.244997998

Simplifying
x + 3 = -6.244997998

Reorder the terms:
3 + x = -6.244997998

Solving
3 + x = -6.244997998

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 = -6.244997998 + -3

Combine like terms: 3 + -3 = 0
0 + x = -6.244997998 + -3
x = -6.244997998 + -3

Combine like terms: -6.244997998 + -3 = -9.244997998
x = -9.244997998

Simplifying
x = -9.244997998


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.244997998, -9.244997998}
Solution
x = {3.244997998, -9.244997998}

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