4(4k+2)8(k-1)=3(2k+4)-1

Solution for 4(4k+2)8(k-1)=3(2k+4)-1 equation:

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

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

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

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

Multiply 4 * 8
32(2 + 4k)(-1 + k) = 3(2k + 4) + -1

Multiply (2 + 4k) * (-1 + k)
32(2(-1 + k) + 4k * (-1 + k)) = 3(2k + 4) + -1
32((-1 * 2 + k * 2) + 4k * (-1 + k)) = 3(2k + 4) + -1
32((-2 + 2k) + 4k * (-1 + k)) = 3(2k + 4) + -1
32(-2 + 2k + (-1 * 4k + k * 4k)) = 3(2k + 4) + -1
32(-2 + 2k + (-4k + 4k2)) = 3(2k + 4) + -1

Combine like terms: 2k + -4k = -2k
32(-2 + -2k + 4k2) = 3(2k + 4) + -1
(-2 * 32 + -2k * 32 + 4k2 * 32) = 3(2k + 4) + -1
(-64 + -64k + 128k2) = 3(2k + 4) + -1

Reorder the terms:
-64 + -64k + 128k2 = 3(4 + 2k) + -1
-64 + -64k + 128k2 = (4 * 3 + 2k * 3) + -1
-64 + -64k + 128k2 = (12 + 6k) + -1

Reorder the terms:
-64 + -64k + 128k2 = 12 + -1 + 6k

Combine like terms: 12 + -1 = 11
-64 + -64k + 128k2 = 11 + 6k

Solving
-64 + -64k + 128k2 = 11 + 6k

Solving for variable 'k'.

Reorder the terms:
-64 + -11 + -64k + -6k + 128k2 = 11 + 6k + -11 + -6k

Combine like terms: -64 + -11 = -75
-75 + -64k + -6k + 128k2 = 11 + 6k + -11 + -6k

Combine like terms: -64k + -6k = -70k
-75 + -70k + 128k2 = 11 + 6k + -11 + -6k

Reorder the terms:
-75 + -70k + 128k2 = 11 + -11 + 6k + -6k

Combine like terms: 11 + -11 = 0
-75 + -70k + 128k2 = 0 + 6k + -6k
-75 + -70k + 128k2 = 6k + -6k

Combine like terms: 6k + -6k = 0
-75 + -70k + 128k2 = 0

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

Divide each side by '128'.
-0.5859375 + -0.546875k + k2 = 0

Move the constant term to the right:

Add '0.5859375' to each side of the equation.
-0.5859375 + -0.546875k + 0.5859375 + k2 = 0 + 0.5859375

Reorder the terms:
-0.5859375 + 0.5859375 + -0.546875k + k2 = 0 + 0.5859375

Combine like terms: -0.5859375 + 0.5859375 = 0.0000000
0.0000000 + -0.546875k + k2 = 0 + 0.5859375
-0.546875k + k2 = 0 + 0.5859375

Combine like terms: 0 + 0.5859375 = 0.5859375
-0.546875k + k2 = 0.5859375

The k term is -0.546875k.  Take half its coefficient (-0.2734375).
Square it (0.07476806641) and add it to both sides.

Add '0.07476806641' to each side of the equation.
-0.546875k + 0.07476806641 + k2 = 0.5859375 + 0.07476806641

Reorder the terms:
0.07476806641 + -0.546875k + k2 = 0.5859375 + 0.07476806641

Combine like terms: 0.5859375 + 0.07476806641 = 0.66070556641
0.07476806641 + -0.546875k + k2 = 0.66070556641

Factor a perfect square on the left side:
(k + -0.2734375)(k + -0.2734375) = 0.66070556641

Calculate the square root of the right side: 0.812837971

Break this problem into two subproblems by setting 
(k + -0.2734375) equal to 0.812837971 and -0.812837971.

Subproblem 1
k + -0.2734375 = 0.812837971

Simplifying
k + -0.2734375 = 0.812837971

Reorder the terms:
-0.2734375 + k = 0.812837971

Solving
-0.2734375 + k = 0.812837971

Solving for variable 'k'.

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

Add '0.2734375' to each side of the equation.
-0.2734375 + 0.2734375 + k = 0.812837971 + 0.2734375

Combine like terms: -0.2734375 + 0.2734375 = 0.0000000
0.0000000 + k = 0.812837971 + 0.2734375
k = 0.812837971 + 0.2734375

Combine like terms: 0.812837971 + 0.2734375 = 1.086275471
k = 1.086275471

Simplifying
k = 1.086275471

Subproblem 2
k + -0.2734375 = -0.812837971

Simplifying
k + -0.2734375 = -0.812837971

Reorder the terms:
-0.2734375 + k = -0.812837971

Solving
-0.2734375 + k = -0.812837971

Solving for variable 'k'.

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

Add '0.2734375' to each side of the equation.
-0.2734375 + 0.2734375 + k = -0.812837971 + 0.2734375

Combine like terms: -0.2734375 + 0.2734375 = 0.0000000
0.0000000 + k = -0.812837971 + 0.2734375
k = -0.812837971 + 0.2734375

Combine like terms: -0.812837971 + 0.2734375 = -0.539400471
k = -0.539400471

Simplifying
k = -0.539400471

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.086275471, -0.539400471}