780=(2x-6)(x-8)

Solution for 780=(2x-6)(x-8) equation:

Simplifying
780 = (2x + -6)(x + -8)

Reorder the terms:
780 = (-6 + 2x)(x + -8)

Reorder the terms:
780 = (-6 + 2x)(-8 + x)

Multiply (-6 + 2x) * (-8 + x)
780 = (-6(-8 + x) + 2x * (-8 + x))
780 = ((-8 * -6 + x * -6) + 2x * (-8 + x))
780 = ((48 + -6x) + 2x * (-8 + x))
780 = (48 + -6x + (-8 * 2x + x * 2x))
780 = (48 + -6x + (-16x + 2x2))

Combine like terms: -6x + -16x = -22x
780 = (48 + -22x + 2x2)

Solving
780 = 48 + -22x + 2x2

Solving for variable 'x'.

Combine like terms: 780 + -48 = 732
732 + 22x + -2x2 = 48 + -22x + 2x2 + -48 + 22x + -2x2

Reorder the terms:
732 + 22x + -2x2 = 48 + -48 + -22x + 22x + 2x2 + -2x2

Combine like terms: 48 + -48 = 0
732 + 22x + -2x2 = 0 + -22x + 22x + 2x2 + -2x2
732 + 22x + -2x2 = -22x + 22x + 2x2 + -2x2

Combine like terms: -22x + 22x = 0
732 + 22x + -2x2 = 0 + 2x2 + -2x2
732 + 22x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
732 + 22x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(366 + 11x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(366 + 11x + -1x2)' equal to zero and attempt to solve:

Simplifying
366 + 11x + -1x2 = 0

Solving
366 + 11x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-366 + -11x + x2 = 0

Move the constant term to the right:

Add '366' to each side of the equation.
-366 + -11x + 366 + x2 = 0 + 366

Reorder the terms:
-366 + 366 + -11x + x2 = 0 + 366

Combine like terms: -366 + 366 = 0
0 + -11x + x2 = 0 + 366
-11x + x2 = 0 + 366

Combine like terms: 0 + 366 = 366
-11x + x2 = 366

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = 366 + 30.25

Reorder the terms:
30.25 + -11x + x2 = 366 + 30.25

Combine like terms: 366 + 30.25 = 396.25
30.25 + -11x + x2 = 396.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 396.25

Calculate the square root of the right side: 19.906029237

Break this problem into two subproblems by setting 
(x + -5.5) equal to 19.906029237 and -19.906029237.

Subproblem 1
x + -5.5 = 19.906029237

Simplifying
x + -5.5 = 19.906029237

Reorder the terms:
-5.5 + x = 19.906029237

Solving
-5.5 + x = 19.906029237

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 19.906029237 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 19.906029237 + 5.5
x = 19.906029237 + 5.5

Combine like terms: 19.906029237 + 5.5 = 25.406029237
x = 25.406029237

Simplifying
x = 25.406029237

Subproblem 2
x + -5.5 = -19.906029237

Simplifying
x + -5.5 = -19.906029237

Reorder the terms:
-5.5 + x = -19.906029237

Solving
-5.5 + x = -19.906029237

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -19.906029237 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -19.906029237 + 5.5
x = -19.906029237 + 5.5

Combine like terms: -19.906029237 + 5.5 = -14.406029237
x = -14.406029237

Simplifying
x = -14.406029237

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.406029237, -14.406029237}
Solution
x = {25.406029237, -14.406029237}