-120(x+20)2x=200

Solution for -120(x+20)2x=200 equation:

Simplifying
-120(x + 20) * 2x = 200

Reorder the terms:
-120(20 + x) * 2x = 200

Reorder the terms for easier multiplication:
-120 * 2x(20 + x) = 200

Multiply -120 * 2
-240x(20 + x) = 200
(20 * -240x + x * -240x) = 200
(-4800x + -240x2) = 200

Solving
-4800x + -240x2 = 200

Solving for variable 'x'.

Reorder the terms:
-200 + -4800x + -240x2 = 200 + -200

Combine like terms: 200 + -200 = 0
-200 + -4800x + -240x2 = 0

Factor out the Greatest Common Factor (GCF), '-40'.
-40(5 + 120x + 6x2) = 0

Ignore the factor -40.
Subproblem 1
Set the factor '(5 + 120x + 6x2)' equal to zero and attempt to solve:

Simplifying
5 + 120x + 6x2 = 0

Solving
5 + 120x + 6x2 = 0

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

Divide each side by '6'.
0.8333333333 + 20x + x2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + 20x + -0.8333333333 + x2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + 20x + x2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + 20x + x2 = 0 + -0.8333333333
20x + x2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
20x + x2 = -0.8333333333

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 = -0.8333333333 + 100

Reorder the terms:
100 + 20x + x2 = -0.8333333333 + 100

Combine like terms: -0.8333333333 + 100 = 99.1666666667
100 + 20x + x2 = 99.1666666667

Factor a perfect square on the left side:
(x + 10)(x + 10) = 99.1666666667

Calculate the square root of the right side: 9.958246164

Break this problem into two subproblems by setting 
(x + 10) equal to 9.958246164 and -9.958246164.

Subproblem 1
x + 10 = 9.958246164

Simplifying
x + 10 = 9.958246164

Reorder the terms:
10 + x = 9.958246164

Solving
10 + x = 9.958246164

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 = 9.958246164 + -10

Combine like terms: 10 + -10 = 0
0 + x = 9.958246164 + -10
x = 9.958246164 + -10

Combine like terms: 9.958246164 + -10 = -0.041753836
x = -0.041753836

Simplifying
x = -0.041753836

Subproblem 2
x + 10 = -9.958246164

Simplifying
x + 10 = -9.958246164

Reorder the terms:
10 + x = -9.958246164

Solving
10 + x = -9.958246164

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 = -9.958246164 + -10

Combine like terms: 10 + -10 = 0
0 + x = -9.958246164 + -10
x = -9.958246164 + -10

Combine like terms: -9.958246164 + -10 = -19.958246164
x = -19.958246164

Simplifying
x = -19.958246164

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.041753836, -19.958246164}
Solution
x = {-0.041753836, -19.958246164}