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

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

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

Reorder the terms:
-4x(-3 + x) = 2(x + -8)
(-3 * -4x + x * -4x) = 2(x + -8)
(12x + -4x2) = 2(x + -8)

Reorder the terms:
12x + -4x2 = 2(-8 + x)
12x + -4x2 = (-8 * 2 + x * 2)
12x + -4x2 = (-16 + 2x)

Solving
12x + -4x2 = -16 + 2x

Solving for variable 'x'.

Reorder the terms:
16 + 12x + -2x + -4x2 = -16 + 2x + 16 + -2x

Combine like terms: 12x + -2x = 10x
16 + 10x + -4x2 = -16 + 2x + 16 + -2x

Reorder the terms:
16 + 10x + -4x2 = -16 + 16 + 2x + -2x

Combine like terms: -16 + 16 = 0
16 + 10x + -4x2 = 0 + 2x + -2x
16 + 10x + -4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
16 + 10x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 5x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + 5x + -2x2)' equal to zero and attempt to solve:

Simplifying
8 + 5x + -2x2 = 0

Solving
8 + 5x + -2x2 = 0

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

Divide each side by '-2'.
-4 + -2.5x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -2.5x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -2.5x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -2.5x + x2 = 0 + 4
-2.5x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-2.5x + x2 = 4

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 = 4 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 4 + 1.5625

Combine like terms: 4 + 1.5625 = 5.5625
1.5625 + -2.5x + x2 = 5.5625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 5.5625

Calculate the square root of the right side: 2.358495283

Break this problem into two subproblems by setting 
(x + -1.25) equal to 2.358495283 and -2.358495283.

Subproblem 1
x + -1.25 = 2.358495283

Simplifying
x + -1.25 = 2.358495283

Reorder the terms:
-1.25 + x = 2.358495283

Solving
-1.25 + x = 2.358495283

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 = 2.358495283 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 2.358495283 + 1.25
x = 2.358495283 + 1.25

Combine like terms: 2.358495283 + 1.25 = 3.608495283
x = 3.608495283

Simplifying
x = 3.608495283

Subproblem 2
x + -1.25 = -2.358495283

Simplifying
x + -1.25 = -2.358495283

Reorder the terms:
-1.25 + x = -2.358495283

Solving
-1.25 + x = -2.358495283

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 = -2.358495283 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -2.358495283 + 1.25
x = -2.358495283 + 1.25

Combine like terms: -2.358495283 + 1.25 = -1.108495283
x = -1.108495283

Simplifying
x = -1.108495283

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.608495283, -1.108495283}
Solution
x = {3.608495283, -1.108495283}