6(x-5)4x=20

Solution for 6(x-5)4x=20 equation:

Simplifying
6(x + -5) * 4x = 20

Reorder the terms:
6(-5 + x) * 4x = 20

Reorder the terms for easier multiplication:
6 * 4x(-5 + x) = 20

Multiply 6 * 4
24x(-5 + x) = 20
(-5 * 24x + x * 24x) = 20
(-120x + 24x2) = 20

Solving
-120x + 24x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + -120x + 24x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + -120x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + -30x + 6x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-5 + -30x + 6x2)' equal to zero and attempt to solve:

Simplifying
-5 + -30x + 6x2 = 0

Solving
-5 + -30x + 6x2 = 0

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

Divide each side by '6'.
-0.8333333333 + -5x + x2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -5x + 0.8333333333 + x2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -5x + x2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -5x + x2 = 0 + 0.8333333333
-5x + x2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-5x + x2 = 0.8333333333

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 0.8333333333 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 0.8333333333 + 6.25

Combine like terms: 0.8333333333 + 6.25 = 7.0833333333
6.25 + -5x + x2 = 7.0833333333

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 7.0833333333

Calculate the square root of the right side: 2.661453237

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.661453237 and -2.661453237.

Subproblem 1
x + -2.5 = 2.661453237

Simplifying
x + -2.5 = 2.661453237

Reorder the terms:
-2.5 + x = 2.661453237

Solving
-2.5 + x = 2.661453237

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 2.661453237 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.661453237 + 2.5
x = 2.661453237 + 2.5

Combine like terms: 2.661453237 + 2.5 = 5.161453237
x = 5.161453237

Simplifying
x = 5.161453237

Subproblem 2
x + -2.5 = -2.661453237

Simplifying
x + -2.5 = -2.661453237

Reorder the terms:
-2.5 + x = -2.661453237

Solving
-2.5 + x = -2.661453237

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -2.661453237 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.661453237 + 2.5
x = -2.661453237 + 2.5

Combine like terms: -2.661453237 + 2.5 = -0.161453237
x = -0.161453237

Simplifying
x = -0.161453237

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.161453237, -0.161453237}
Solution
x = {5.161453237, -0.161453237}