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

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

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

Reorder the terms:
2x(-3 + 4x) + -8 = 4 + 2x
(-3 * 2x + 4x * 2x) + -8 = 4 + 2x
(-6x + 8x2) + -8 = 4 + 2x

Reorder the terms:
-8 + -6x + 8x2 = 4 + 2x

Solving
-8 + -6x + 8x2 = 4 + 2x

Solving for variable 'x'.

Reorder the terms:
-8 + -4 + -6x + -2x + 8x2 = 4 + 2x + -4 + -2x

Combine like terms: -8 + -4 = -12
-12 + -6x + -2x + 8x2 = 4 + 2x + -4 + -2x

Combine like terms: -6x + -2x = -8x
-12 + -8x + 8x2 = 4 + 2x + -4 + -2x

Reorder the terms:
-12 + -8x + 8x2 = 4 + -4 + 2x + -2x

Combine like terms: 4 + -4 = 0
-12 + -8x + 8x2 = 0 + 2x + -2x
-12 + -8x + 8x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-12 + -8x + 8x2 = 0

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

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

Simplifying
-3 + -2x + 2x2 = 0

Solving
-3 + -2x + 2x2 = 0

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

Divide each side by '2'.
-1.5 + -1x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -1x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -1x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -1x + x2 = 0 + 1.5
-1x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-1x + x2 = 1.5

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 1.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 1.5 + 0.25

Combine like terms: 1.5 + 0.25 = 1.75
0.25 + -1x + x2 = 1.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.322875656 and -1.322875656.

Subproblem 1
x + -0.5 = 1.322875656

Simplifying
x + -0.5 = 1.322875656

Reorder the terms:
-0.5 + x = 1.322875656

Solving
-0.5 + x = 1.322875656

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 1.322875656 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1.322875656 + 0.5
x = 1.322875656 + 0.5

Combine like terms: 1.322875656 + 0.5 = 1.822875656
x = 1.822875656

Simplifying
x = 1.822875656

Subproblem 2
x + -0.5 = -1.322875656

Simplifying
x + -0.5 = -1.322875656

Reorder the terms:
-0.5 + x = -1.322875656

Solving
-0.5 + x = -1.322875656

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -1.322875656 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1.322875656 + 0.5
x = -1.322875656 + 0.5

Combine like terms: -1.322875656 + 0.5 = -0.822875656
x = -0.822875656

Simplifying
x = -0.822875656

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.822875656, -0.822875656}
Solution
x = {1.822875656, -0.822875656}