-4(1+8k)=-7k(7k-3)

Solution for -4(1+8k)=-7k(7k-3) equation:

Simplifying
-4(1 + 8k) = -7k(7k + -3)
(1 * -4 + 8k * -4) = -7k(7k + -3)
(-4 + -32k) = -7k(7k + -3)

Reorder the terms:
-4 + -32k = -7k(-3 + 7k)
-4 + -32k = (-3 * -7k + 7k * -7k)
-4 + -32k = (21k + -49k2)

Solving
-4 + -32k = 21k + -49k2

Solving for variable 'k'.

Combine like terms: -32k + -21k = -53k
-4 + -53k + 49k2 = 21k + -49k2 + -21k + 49k2

Reorder the terms:
-4 + -53k + 49k2 = 21k + -21k + -49k2 + 49k2

Combine like terms: 21k + -21k = 0
-4 + -53k + 49k2 = 0 + -49k2 + 49k2
-4 + -53k + 49k2 = -49k2 + 49k2

Combine like terms: -49k2 + 49k2 = 0
-4 + -53k + 49k2 = 0

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

Divide each side by '49'.
-0.08163265306 + -1.081632653k + k2 = 0

Move the constant term to the right:

Add '0.08163265306' to each side of the equation.
-0.08163265306 + -1.081632653k + 0.08163265306 + k2 = 0 + 0.08163265306

Reorder the terms:
-0.08163265306 + 0.08163265306 + -1.081632653k + k2 = 0 + 0.08163265306

Combine like terms: -0.08163265306 + 0.08163265306 = 0.00000000000
0.00000000000 + -1.081632653k + k2 = 0 + 0.08163265306
-1.081632653k + k2 = 0 + 0.08163265306

Combine like terms: 0 + 0.08163265306 = 0.08163265306
-1.081632653k + k2 = 0.08163265306

The k term is -1.081632653k.  Take half its coefficient (-0.5408163265).
Square it (0.2924822990) and add it to both sides.

Add '0.2924822990' to each side of the equation.
-1.081632653k + 0.2924822990 + k2 = 0.08163265306 + 0.2924822990

Reorder the terms:
0.2924822990 + -1.081632653k + k2 = 0.08163265306 + 0.2924822990

Combine like terms: 0.08163265306 + 0.2924822990 = 0.37411495206
0.2924822990 + -1.081632653k + k2 = 0.37411495206

Factor a perfect square on the left side:
(k + -0.5408163265)(k + -0.5408163265) = 0.37411495206

Calculate the square root of the right side: 0.61164937

Break this problem into two subproblems by setting 
(k + -0.5408163265) equal to 0.61164937 and -0.61164937.

Subproblem 1
k + -0.5408163265 = 0.61164937

Simplifying
k + -0.5408163265 = 0.61164937

Reorder the terms:
-0.5408163265 + k = 0.61164937

Solving
-0.5408163265 + k = 0.61164937

Solving for variable 'k'.

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

Add '0.5408163265' to each side of the equation.
-0.5408163265 + 0.5408163265 + k = 0.61164937 + 0.5408163265

Combine like terms: -0.5408163265 + 0.5408163265 = 0.0000000000
0.0000000000 + k = 0.61164937 + 0.5408163265
k = 0.61164937 + 0.5408163265

Combine like terms: 0.61164937 + 0.5408163265 = 1.1524656965
k = 1.1524656965

Simplifying
k = 1.1524656965

Subproblem 2
k + -0.5408163265 = -0.61164937

Simplifying
k + -0.5408163265 = -0.61164937

Reorder the terms:
-0.5408163265 + k = -0.61164937

Solving
-0.5408163265 + k = -0.61164937

Solving for variable 'k'.

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

Add '0.5408163265' to each side of the equation.
-0.5408163265 + 0.5408163265 + k = -0.61164937 + 0.5408163265

Combine like terms: -0.5408163265 + 0.5408163265 = 0.0000000000
0.0000000000 + k = -0.61164937 + 0.5408163265
k = -0.61164937 + 0.5408163265

Combine like terms: -0.61164937 + 0.5408163265 = -0.0708330435
k = -0.0708330435

Simplifying
k = -0.0708330435

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.1524656965, -0.0708330435}