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

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

Simplifying
3(2x + -8) = 4x(x + -8)

Reorder the terms:
3(-8 + 2x) = 4x(x + -8)
(-8 * 3 + 2x * 3) = 4x(x + -8)
(-24 + 6x) = 4x(x + -8)

Reorder the terms:
-24 + 6x = 4x(-8 + x)
-24 + 6x = (-8 * 4x + x * 4x)
-24 + 6x = (-32x + 4x2)

Solving
-24 + 6x = -32x + 4x2

Solving for variable 'x'.

Combine like terms: 6x + 32x = 38x
-24 + 38x + -4x2 = -32x + 4x2 + 32x + -4x2

Reorder the terms:
-24 + 38x + -4x2 = -32x + 32x + 4x2 + -4x2

Combine like terms: -32x + 32x = 0
-24 + 38x + -4x2 = 0 + 4x2 + -4x2
-24 + 38x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-24 + 38x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 19x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-12 + 19x + -2x2)' equal to zero and attempt to solve:

Simplifying
-12 + 19x + -2x2 = 0

Solving
-12 + 19x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
6 + -9.5x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -9.5x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -9.5x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -9.5x + x2 = 0 + -6
-9.5x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-9.5x + x2 = -6

The x term is -9.5x.  Take half its coefficient (-4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
-9.5x + 22.5625 + x2 = -6 + 22.5625

Reorder the terms:
22.5625 + -9.5x + x2 = -6 + 22.5625

Combine like terms: -6 + 22.5625 = 16.5625
22.5625 + -9.5x + x2 = 16.5625

Factor a perfect square on the left side:
(x + -4.75)(x + -4.75) = 16.5625

Calculate the square root of the right side: 4.069705149

Break this problem into two subproblems by setting 
(x + -4.75) equal to 4.069705149 and -4.069705149.

Subproblem 1
x + -4.75 = 4.069705149

Simplifying
x + -4.75 = 4.069705149

Reorder the terms:
-4.75 + x = 4.069705149

Solving
-4.75 + x = 4.069705149

Solving for variable 'x'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + x = 4.069705149 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + x = 4.069705149 + 4.75
x = 4.069705149 + 4.75

Combine like terms: 4.069705149 + 4.75 = 8.819705149
x = 8.819705149

Simplifying
x = 8.819705149

Subproblem 2
x + -4.75 = -4.069705149

Simplifying
x + -4.75 = -4.069705149

Reorder the terms:
-4.75 + x = -4.069705149

Solving
-4.75 + x = -4.069705149

Solving for variable 'x'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + x = -4.069705149 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + x = -4.069705149 + 4.75
x = -4.069705149 + 4.75

Combine like terms: -4.069705149 + 4.75 = 0.680294851
x = 0.680294851

Simplifying
x = 0.680294851

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.819705149, 0.680294851}
Solution
x = {8.819705149, 0.680294851}