(2k^2+4k)-(5k^2-2)-(k^2-8k-6)=

Solution for (2k^2+4k)-(5k^2-2)-(k^2-8k-6)= equation:

Simplifying
(2k2 + 4k) + -1(5k2 + -2) + -1(k2 + -8k + -6) = 0

Reorder the terms:
(4k + 2k2) + -1(5k2 + -2) + -1(k2 + -8k + -6) = 0

Remove parenthesis around (4k + 2k2)
4k + 2k2 + -1(5k2 + -2) + -1(k2 + -8k + -6) = 0

Reorder the terms:
4k + 2k2 + -1(-2 + 5k2) + -1(k2 + -8k + -6) = 0
4k + 2k2 + (-2 * -1 + 5k2 * -1) + -1(k2 + -8k + -6) = 0
4k + 2k2 + (2 + -5k2) + -1(k2 + -8k + -6) = 0

Reorder the terms:
4k + 2k2 + 2 + -5k2 + -1(-6 + -8k + k2) = 0
4k + 2k2 + 2 + -5k2 + (-6 * -1 + -8k * -1 + k2 * -1) = 0
4k + 2k2 + 2 + -5k2 + (6 + 8k + -1k2) = 0

Reorder the terms:
2 + 6 + 4k + 8k + 2k2 + -5k2 + -1k2 = 0

Combine like terms: 2 + 6 = 8
8 + 4k + 8k + 2k2 + -5k2 + -1k2 = 0

Combine like terms: 4k + 8k = 12k
8 + 12k + 2k2 + -5k2 + -1k2 = 0

Combine like terms: 2k2 + -5k2 = -3k2
8 + 12k + -3k2 + -1k2 = 0

Combine like terms: -3k2 + -1k2 = -4k2
8 + 12k + -4k2 = 0

Solving
8 + 12k + -4k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + 3k + -1k2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(2 + 3k + -1k2)' equal to zero and attempt to solve:

Simplifying
2 + 3k + -1k2 = 0

Solving
2 + 3k + -1k2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2 + -3k + k2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -3k + 2 + k2 = 0 + 2

Reorder the terms:
-2 + 2 + -3k + k2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3k + k2 = 0 + 2
-3k + k2 = 0 + 2

Combine like terms: 0 + 2 = 2
-3k + k2 = 2

The k term is -3k.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3k + 2.25 + k2 = 2 + 2.25

Reorder the terms:
2.25 + -3k + k2 = 2 + 2.25

Combine like terms: 2 + 2.25 = 4.25
2.25 + -3k + k2 = 4.25

Factor a perfect square on the left side:
(k + -1.5)(k + -1.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(k + -1.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
k + -1.5 = 2.061552813

Simplifying
k + -1.5 = 2.061552813

Reorder the terms:
-1.5 + k = 2.061552813

Solving
-1.5 + k = 2.061552813

Solving for variable 'k'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + k = 2.061552813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + k = 2.061552813 + 1.5
k = 2.061552813 + 1.5

Combine like terms: 2.061552813 + 1.5 = 3.561552813
k = 3.561552813

Simplifying
k = 3.561552813

Subproblem 2
k + -1.5 = -2.061552813

Simplifying
k + -1.5 = -2.061552813

Reorder the terms:
-1.5 + k = -2.061552813

Solving
-1.5 + k = -2.061552813

Solving for variable 'k'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + k = -2.061552813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + k = -2.061552813 + 1.5
k = -2.061552813 + 1.5

Combine like terms: -2.061552813 + 1.5 = -0.561552813
k = -0.561552813

Simplifying
k = -0.561552813

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {3.561552813, -0.561552813}
Solution
k = {3.561552813, -0.561552813}