6x-4(2x-8)=2x(-x+1)

Solution for 6x-4(2x-8)=2x(-x+1) equation:

Simplifying
6x + -4(2x + -8) = 2x(-1x + 1)

Reorder the terms:
6x + -4(-8 + 2x) = 2x(-1x + 1)
6x + (-8 * -4 + 2x * -4) = 2x(-1x + 1)
6x + (32 + -8x) = 2x(-1x + 1)

Reorder the terms:
32 + 6x + -8x = 2x(-1x + 1)

Combine like terms: 6x + -8x = -2x
32 + -2x = 2x(-1x + 1)

Reorder the terms:
32 + -2x = 2x(1 + -1x)
32 + -2x = (1 * 2x + -1x * 2x)
32 + -2x = (2x + -2x2)

Solving
32 + -2x = 2x + -2x2

Solving for variable 'x'.

Combine like terms: -2x + -2x = -4x
32 + -4x + 2x2 = 2x + -2x2 + -2x + 2x2

Reorder the terms:
32 + -4x + 2x2 = 2x + -2x + -2x2 + 2x2

Combine like terms: 2x + -2x = 0
32 + -4x + 2x2 = 0 + -2x2 + 2x2
32 + -4x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
32 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -2x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(16 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
16 + -2x + x2 = 0

Solving
16 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -2x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -2x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -2x + x2 = 0 + -16
-2x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-2x + x2 = -16

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 = -16 + 1

Reorder the terms:
1 + -2x + x2 = -16 + 1

Combine like terms: -16 + 1 = -15
1 + -2x + x2 = -15

Factor a perfect square on the left side:
(x + -1)(x + -1) = -15

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.