4k+7(-4-2k)=-2k(k-2)

Solution for 4k+7(-4-2k)=-2k(k-2) equation:

Simplifying
4k + 7(-4 + -2k) = -2k(k + -2)
4k + (-4 * 7 + -2k * 7) = -2k(k + -2)
4k + (-28 + -14k) = -2k(k + -2)

Reorder the terms:
-28 + 4k + -14k = -2k(k + -2)

Combine like terms: 4k + -14k = -10k
-28 + -10k = -2k(k + -2)

Reorder the terms:
-28 + -10k = -2k(-2 + k)
-28 + -10k = (-2 * -2k + k * -2k)
-28 + -10k = (4k + -2k2)

Solving
-28 + -10k = 4k + -2k2

Solving for variable 'k'.

Combine like terms: -10k + -4k = -14k
-28 + -14k + 2k2 = 4k + -2k2 + -4k + 2k2

Reorder the terms:
-28 + -14k + 2k2 = 4k + -4k + -2k2 + 2k2

Combine like terms: 4k + -4k = 0
-28 + -14k + 2k2 = 0 + -2k2 + 2k2
-28 + -14k + 2k2 = -2k2 + 2k2

Combine like terms: -2k2 + 2k2 = 0
-28 + -14k + 2k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + -7k + k2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-14 + -7k + k2)' equal to zero and attempt to solve:

Simplifying
-14 + -7k + k2 = 0

Solving
-14 + -7k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -7k + 14 + k2 = 0 + 14

Reorder the terms:
-14 + 14 + -7k + k2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -7k + k2 = 0 + 14
-7k + k2 = 0 + 14

Combine like terms: 0 + 14 = 14
-7k + k2 = 14

The k term is -7k.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7k + 12.25 + k2 = 14 + 12.25

Reorder the terms:
12.25 + -7k + k2 = 14 + 12.25

Combine like terms: 14 + 12.25 = 26.25
12.25 + -7k + k2 = 26.25

Factor a perfect square on the left side:
(k + -3.5)(k + -3.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(k + -3.5) equal to 5.123475383 and -5.123475383.

Subproblem 1
k + -3.5 = 5.123475383

Simplifying
k + -3.5 = 5.123475383

Reorder the terms:
-3.5 + k = 5.123475383

Solving
-3.5 + k = 5.123475383

Solving for variable 'k'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + k = 5.123475383 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + k = 5.123475383 + 3.5
k = 5.123475383 + 3.5

Combine like terms: 5.123475383 + 3.5 = 8.623475383
k = 8.623475383

Simplifying
k = 8.623475383

Subproblem 2
k + -3.5 = -5.123475383

Simplifying
k + -3.5 = -5.123475383

Reorder the terms:
-3.5 + k = -5.123475383

Solving
-3.5 + k = -5.123475383

Solving for variable 'k'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + k = -5.123475383 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + k = -5.123475383 + 3.5
k = -5.123475383 + 3.5

Combine like terms: -5.123475383 + 3.5 = -1.623475383
k = -1.623475383

Simplifying
k = -1.623475383

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {8.623475383, -1.623475383}
Solution
k = {8.623475383, -1.623475383}