8x(x+6)-2(-24)=20(20x-4)

Solution for 8x(x+6)-2(-24)=20(20x-4) equation:

Simplifying
8x(x + 6) + -2(-24) = 20(20x + -4)

Reorder the terms:
8x(6 + x) + -2(-24) = 20(20x + -4)
(6 * 8x + x * 8x) + -2(-24) = 20(20x + -4)
(48x + 8x2) + -2(-24) = 20(20x + -4)

Multiply -2 * -24
48x + 8x2 + 48 = 20(20x + -4)

Reorder the terms:
48 + 48x + 8x2 = 20(20x + -4)

Reorder the terms:
48 + 48x + 8x2 = 20(-4 + 20x)
48 + 48x + 8x2 = (-4 * 20 + 20x * 20)
48 + 48x + 8x2 = (-80 + 400x)

Solving
48 + 48x + 8x2 = -80 + 400x

Solving for variable 'x'.

Reorder the terms:
48 + 80 + 48x + -400x + 8x2 = -80 + 400x + 80 + -400x

Combine like terms: 48 + 80 = 128
128 + 48x + -400x + 8x2 = -80 + 400x + 80 + -400x

Combine like terms: 48x + -400x = -352x
128 + -352x + 8x2 = -80 + 400x + 80 + -400x

Reorder the terms:
128 + -352x + 8x2 = -80 + 80 + 400x + -400x

Combine like terms: -80 + 80 = 0
128 + -352x + 8x2 = 0 + 400x + -400x
128 + -352x + 8x2 = 400x + -400x

Combine like terms: 400x + -400x = 0
128 + -352x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(16 + -44x + x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(16 + -44x + x2)' equal to zero and attempt to solve:

Simplifying
16 + -44x + x2 = 0

Solving
16 + -44x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -44x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -44x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -44x + x2 = 0 + -16
-44x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-44x + x2 = -16

The x term is -44x.  Take half its coefficient (-22).
Square it (484) and add it to both sides.

Add '484' to each side of the equation.
-44x + 484 + x2 = -16 + 484

Reorder the terms:
484 + -44x + x2 = -16 + 484

Combine like terms: -16 + 484 = 468
484 + -44x + x2 = 468

Factor a perfect square on the left side:
(x + -22)(x + -22) = 468

Calculate the square root of the right side: 21.633307653

Break this problem into two subproblems by setting 
(x + -22) equal to 21.633307653 and -21.633307653.

Subproblem 1
x + -22 = 21.633307653

Simplifying
x + -22 = 21.633307653

Reorder the terms:
-22 + x = 21.633307653

Solving
-22 + x = 21.633307653

Solving for variable 'x'.

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

Add '22' to each side of the equation.
-22 + 22 + x = 21.633307653 + 22

Combine like terms: -22 + 22 = 0
0 + x = 21.633307653 + 22
x = 21.633307653 + 22

Combine like terms: 21.633307653 + 22 = 43.633307653
x = 43.633307653

Simplifying
x = 43.633307653

Subproblem 2
x + -22 = -21.633307653

Simplifying
x + -22 = -21.633307653

Reorder the terms:
-22 + x = -21.633307653

Solving
-22 + x = -21.633307653

Solving for variable 'x'.

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

Add '22' to each side of the equation.
-22 + 22 + x = -21.633307653 + 22

Combine like terms: -22 + 22 = 0
0 + x = -21.633307653 + 22
x = -21.633307653 + 22

Combine like terms: -21.633307653 + 22 = 0.366692347
x = 0.366692347

Simplifying
x = 0.366692347

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {43.633307653, 0.366692347}
Solution
x = {43.633307653, 0.366692347}