(x[x+12])*2=60*2

Solution for (x[x+12])*2=60*2 equation:

Simplifying
(x[x + 12]) * 2 = 60 * 2

Reorder the terms:
(x[12 + x]) * 2 = 60 * 2
([12 * x + x * x]) * 2 = 60 * 2
([12x + x2]) * 2 = 60 * 2

Reorder the terms for easier multiplication:
2(12x + x2) = 60 * 2
(12x * 2 + x2 * 2) = 60 * 2
(24x + 2x2) = 60 * 2

Multiply 60 * 2
24x + 2x2 = 120

Solving
24x + 2x2 = 120

Solving for variable 'x'.

Reorder the terms:
-120 + 24x + 2x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 24x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-60 + 12x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-60 + 12x + x2)' equal to zero and attempt to solve:

Simplifying
-60 + 12x + x2 = 0

Solving
-60 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 12x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 12x + x2 = 0 + 60

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

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

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 60 + 36

Reorder the terms:
36 + 12x + x2 = 60 + 36

Combine like terms: 60 + 36 = 96
36 + 12x + x2 = 96

Factor a perfect square on the left side:
(x + 6)(x + 6) = 96

Calculate the square root of the right side: 9.797958971

Break this problem into two subproblems by setting 
(x + 6) equal to 9.797958971 and -9.797958971.

Subproblem 1
x + 6 = 9.797958971

Simplifying
x + 6 = 9.797958971

Reorder the terms:
6 + x = 9.797958971

Solving
6 + x = 9.797958971

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 9.797958971 + -6

Combine like terms: 6 + -6 = 0
0 + x = 9.797958971 + -6
x = 9.797958971 + -6

Combine like terms: 9.797958971 + -6 = 3.797958971
x = 3.797958971

Simplifying
x = 3.797958971

Subproblem 2
x + 6 = -9.797958971

Simplifying
x + 6 = -9.797958971

Reorder the terms:
6 + x = -9.797958971

Solving
6 + x = -9.797958971

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -9.797958971 + -6

Combine like terms: 6 + -6 = 0
0 + x = -9.797958971 + -6
x = -9.797958971 + -6

Combine like terms: -9.797958971 + -6 = -15.797958971
x = -15.797958971

Simplifying
x = -15.797958971

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.797958971, -15.797958971}
Solution
x = {3.797958971, -15.797958971}