(2x-4)x+6=39(24)

Solution for (2x-4)x+6=39(24) equation:

Simplifying
(2x + -4) * x + 6 = 39(24)

Reorder the terms:
(-4 + 2x) * x + 6 = 39(24)

Reorder the terms for easier multiplication:
x(-4 + 2x) + 6 = 39(24)
(-4 * x + 2x * x) + 6 = 39(24)
(-4x + 2x2) + 6 = 39(24)

Reorder the terms:
6 + -4x + 2x2 = 39(24)

Multiply 39 * 24
6 + -4x + 2x2 = 936

Solving
6 + -4x + 2x2 = 936

Solving for variable 'x'.

Reorder the terms:
6 + -936 + -4x + 2x2 = 936 + -936

Combine like terms: 6 + -936 = -930
-930 + -4x + 2x2 = 936 + -936

Combine like terms: 936 + -936 = 0
-930 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-465 + -2x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-465 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-465 + -2x + x2 = 0

Solving
-465 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '465' to each side of the equation.
-465 + -2x + 465 + x2 = 0 + 465

Reorder the terms:
-465 + 465 + -2x + x2 = 0 + 465

Combine like terms: -465 + 465 = 0
0 + -2x + x2 = 0 + 465
-2x + x2 = 0 + 465

Combine like terms: 0 + 465 = 465
-2x + x2 = 465

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 465 + 1

Reorder the terms:
1 + -2x + x2 = 465 + 1

Combine like terms: 465 + 1 = 466
1 + -2x + x2 = 466

Factor a perfect square on the left side:
(x + -1)(x + -1) = 466

Calculate the square root of the right side: 21.587033145

Break this problem into two subproblems by setting 
(x + -1) equal to 21.587033145 and -21.587033145.

Subproblem 1
x + -1 = 21.587033145

Simplifying
x + -1 = 21.587033145

Reorder the terms:
-1 + x = 21.587033145

Solving
-1 + x = 21.587033145

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 21.587033145 + 1

Combine like terms: -1 + 1 = 0
0 + x = 21.587033145 + 1
x = 21.587033145 + 1

Combine like terms: 21.587033145 + 1 = 22.587033145
x = 22.587033145

Simplifying
x = 22.587033145

Subproblem 2
x + -1 = -21.587033145

Simplifying
x + -1 = -21.587033145

Reorder the terms:
-1 + x = -21.587033145

Solving
-1 + x = -21.587033145

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -21.587033145 + 1

Combine like terms: -1 + 1 = 0
0 + x = -21.587033145 + 1
x = -21.587033145 + 1

Combine like terms: -21.587033145 + 1 = -20.587033145
x = -20.587033145

Simplifying
x = -20.587033145

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.587033145, -20.587033145}
Solution
x = {22.587033145, -20.587033145}