2(3x-120)*(2x)=1040

Solution for 2(3x-120)*(2x)=1040 equation:

Simplifying
2(3x + -120)(2x) = 1040

Reorder the terms:
2(-120 + 3x)(2x) = 1040

Remove parenthesis around (2x)
2(-120 + 3x) * 2x = 1040

Reorder the terms for easier multiplication:
2 * 2x(-120 + 3x) = 1040

Multiply 2 * 2
4x(-120 + 3x) = 1040
(-120 * 4x + 3x * 4x) = 1040
(-480x + 12x2) = 1040

Solving
-480x + 12x2 = 1040

Solving for variable 'x'.

Reorder the terms:
-1040 + -480x + 12x2 = 1040 + -1040

Combine like terms: 1040 + -1040 = 0
-1040 + -480x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-260 + -120x + 3x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-260 + -120x + 3x2)' equal to zero and attempt to solve:

Simplifying
-260 + -120x + 3x2 = 0

Solving
-260 + -120x + 3x2 = 0

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

Divide each side by '3'.
-86.66666667 + -40x + x2 = 0

Move the constant term to the right:

Add '86.66666667' to each side of the equation.
-86.66666667 + -40x + 86.66666667 + x2 = 0 + 86.66666667

Reorder the terms:
-86.66666667 + 86.66666667 + -40x + x2 = 0 + 86.66666667

Combine like terms: -86.66666667 + 86.66666667 = 0.00000000
0.00000000 + -40x + x2 = 0 + 86.66666667
-40x + x2 = 0 + 86.66666667

Combine like terms: 0 + 86.66666667 = 86.66666667
-40x + x2 = 86.66666667

The x term is -40x.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40x + 400 + x2 = 86.66666667 + 400

Reorder the terms:
400 + -40x + x2 = 86.66666667 + 400

Combine like terms: 86.66666667 + 400 = 486.66666667
400 + -40x + x2 = 486.66666667

Factor a perfect square on the left side:
(x + -20)(x + -20) = 486.66666667

Calculate the square root of the right side: 22.06052281

Break this problem into two subproblems by setting 
(x + -20) equal to 22.06052281 and -22.06052281.

Subproblem 1
x + -20 = 22.06052281

Simplifying
x + -20 = 22.06052281

Reorder the terms:
-20 + x = 22.06052281

Solving
-20 + x = 22.06052281

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + x = 22.06052281 + 20

Combine like terms: -20 + 20 = 0
0 + x = 22.06052281 + 20
x = 22.06052281 + 20

Combine like terms: 22.06052281 + 20 = 42.06052281
x = 42.06052281

Simplifying
x = 42.06052281

Subproblem 2
x + -20 = -22.06052281

Simplifying
x + -20 = -22.06052281

Reorder the terms:
-20 + x = -22.06052281

Solving
-20 + x = -22.06052281

Solving for variable 'x'.

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

Add '20' to each side of the equation.
-20 + 20 + x = -22.06052281 + 20

Combine like terms: -20 + 20 = 0
0 + x = -22.06052281 + 20
x = -22.06052281 + 20

Combine like terms: -22.06052281 + 20 = -2.06052281
x = -2.06052281

Simplifying
x = -2.06052281

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {42.06052281, -2.06052281}
Solution
x = {42.06052281, -2.06052281}