2(3x-60)2x=440

Solution for 2(3x-60)2x=440 equation:

Simplifying
2(3x + -60) * 2x = 440

Reorder the terms:
2(-60 + 3x) * 2x = 440

Reorder the terms for easier multiplication:
2 * 2x(-60 + 3x) = 440

Multiply 2 * 2
4x(-60 + 3x) = 440
(-60 * 4x + 3x * 4x) = 440
(-240x + 12x2) = 440

Solving
-240x + 12x2 = 440

Solving for variable 'x'.

Reorder the terms:
-440 + -240x + 12x2 = 440 + -440

Combine like terms: 440 + -440 = 0
-440 + -240x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-110 + -60x + 3x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-110 + -60x + 3x2)' equal to zero and attempt to solve:

Simplifying
-110 + -60x + 3x2 = 0

Solving
-110 + -60x + 3x2 = 0

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

Divide each side by '3'.
-36.66666667 + -20x + x2 = 0

Move the constant term to the right:

Add '36.66666667' to each side of the equation.
-36.66666667 + -20x + 36.66666667 + x2 = 0 + 36.66666667

Reorder the terms:
-36.66666667 + 36.66666667 + -20x + x2 = 0 + 36.66666667

Combine like terms: -36.66666667 + 36.66666667 = 0.00000000
0.00000000 + -20x + x2 = 0 + 36.66666667
-20x + x2 = 0 + 36.66666667

Combine like terms: 0 + 36.66666667 = 36.66666667
-20x + x2 = 36.66666667

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 = 36.66666667 + 100

Reorder the terms:
100 + -20x + x2 = 36.66666667 + 100

Combine like terms: 36.66666667 + 100 = 136.66666667
100 + -20x + x2 = 136.66666667

Factor a perfect square on the left side:
(x + -10)(x + -10) = 136.66666667

Calculate the square root of the right side: 11.690451945

Break this problem into two subproblems by setting 
(x + -10) equal to 11.690451945 and -11.690451945.

Subproblem 1
x + -10 = 11.690451945

Simplifying
x + -10 = 11.690451945

Reorder the terms:
-10 + x = 11.690451945

Solving
-10 + x = 11.690451945

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 = 11.690451945 + 10

Combine like terms: -10 + 10 = 0
0 + x = 11.690451945 + 10
x = 11.690451945 + 10

Combine like terms: 11.690451945 + 10 = 21.690451945
x = 21.690451945

Simplifying
x = 21.690451945

Subproblem 2
x + -10 = -11.690451945

Simplifying
x + -10 = -11.690451945

Reorder the terms:
-10 + x = -11.690451945

Solving
-10 + x = -11.690451945

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 = -11.690451945 + 10

Combine like terms: -10 + 10 = 0
0 + x = -11.690451945 + 10
x = -11.690451945 + 10

Combine like terms: -11.690451945 + 10 = -1.690451945
x = -1.690451945

Simplifying
x = -1.690451945

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.690451945, -1.690451945}
Solution
x = {21.690451945, -1.690451945}