(3x-4)*2-(x-7)*2=8x(x-2)

Solution for (3x-4)*2-(x-7)*2=8x(x-2) equation:

Simplifying
(3x + -4) * 2 + -1(x + -7) * 2 = 8x(x + -2)

Reorder the terms:
(-4 + 3x) * 2 + -1(x + -7) * 2 = 8x(x + -2)

Reorder the terms for easier multiplication:
2(-4 + 3x) + -1(x + -7) * 2 = 8x(x + -2)
(-4 * 2 + 3x * 2) + -1(x + -7) * 2 = 8x(x + -2)
(-8 + 6x) + -1(x + -7) * 2 = 8x(x + -2)

Reorder the terms:
-8 + 6x + -1(-7 + x) * 2 = 8x(x + -2)

Reorder the terms for easier multiplication:
-8 + 6x + -1 * 2(-7 + x) = 8x(x + -2)

Multiply -1 * 2
-8 + 6x + -2(-7 + x) = 8x(x + -2)
-8 + 6x + (-7 * -2 + x * -2) = 8x(x + -2)
-8 + 6x + (14 + -2x) = 8x(x + -2)

Reorder the terms:
-8 + 14 + 6x + -2x = 8x(x + -2)

Combine like terms: -8 + 14 = 6
6 + 6x + -2x = 8x(x + -2)

Combine like terms: 6x + -2x = 4x
6 + 4x = 8x(x + -2)

Reorder the terms:
6 + 4x = 8x(-2 + x)
6 + 4x = (-2 * 8x + x * 8x)
6 + 4x = (-16x + 8x2)

Solving
6 + 4x = -16x + 8x2

Solving for variable 'x'.

Combine like terms: 4x + 16x = 20x
6 + 20x + -8x2 = -16x + 8x2 + 16x + -8x2

Reorder the terms:
6 + 20x + -8x2 = -16x + 16x + 8x2 + -8x2

Combine like terms: -16x + 16x = 0
6 + 20x + -8x2 = 0 + 8x2 + -8x2
6 + 20x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
6 + 20x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 10x + -4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 10x + -4x2)' equal to zero and attempt to solve:

Simplifying
3 + 10x + -4x2 = 0

Solving
3 + 10x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-0.75 + -2.5x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -2.5x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -2.5x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -2.5x + x2 = 0 + 0.75
-2.5x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-2.5x + x2 = 0.75

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 0.75 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 0.75 + 1.5625

Combine like terms: 0.75 + 1.5625 = 2.3125
1.5625 + -2.5x + x2 = 2.3125

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 2.3125

Calculate the square root of the right side: 1.520690633

Break this problem into two subproblems by setting 
(x + -1.25) equal to 1.520690633 and -1.520690633.

Subproblem 1
x + -1.25 = 1.520690633

Simplifying
x + -1.25 = 1.520690633

Reorder the terms:
-1.25 + x = 1.520690633

Solving
-1.25 + x = 1.520690633

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 1.520690633 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 1.520690633 + 1.25
x = 1.520690633 + 1.25

Combine like terms: 1.520690633 + 1.25 = 2.770690633
x = 2.770690633

Simplifying
x = 2.770690633

Subproblem 2
x + -1.25 = -1.520690633

Simplifying
x + -1.25 = -1.520690633

Reorder the terms:
-1.25 + x = -1.520690633

Solving
-1.25 + x = -1.520690633

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -1.520690633 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -1.520690633 + 1.25
x = -1.520690633 + 1.25

Combine like terms: -1.520690633 + 1.25 = -0.270690633
x = -0.270690633

Simplifying
x = -0.270690633

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.770690633, -0.270690633}
Solution
x = {2.770690633, -0.270690633}