6k+4=-2-2k^2+16k

Solution for 6k+4=-2-2k^2+16k equation:

Simplifying
6k + 4 = -2 + -2k2 + 16k

Reorder the terms:
4 + 6k = -2 + -2k2 + 16k

Reorder the terms:
4 + 6k = -2 + 16k + -2k2

Solving
4 + 6k = -2 + 16k + -2k2

Solving for variable 'k'.

Reorder the terms:
4 + 2 + 6k + -16k + 2k2 = -2 + 16k + -2k2 + 2 + -16k + 2k2

Combine like terms: 4 + 2 = 6
6 + 6k + -16k + 2k2 = -2 + 16k + -2k2 + 2 + -16k + 2k2

Combine like terms: 6k + -16k = -10k
6 + -10k + 2k2 = -2 + 16k + -2k2 + 2 + -16k + 2k2

Reorder the terms:
6 + -10k + 2k2 = -2 + 2 + 16k + -16k + -2k2 + 2k2

Combine like terms: -2 + 2 = 0
6 + -10k + 2k2 = 0 + 16k + -16k + -2k2 + 2k2
6 + -10k + 2k2 = 16k + -16k + -2k2 + 2k2

Combine like terms: 16k + -16k = 0
6 + -10k + 2k2 = 0 + -2k2 + 2k2
6 + -10k + 2k2 = -2k2 + 2k2

Combine like terms: -2k2 + 2k2 = 0
6 + -10k + 2k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -5k + k2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -5k + k2)' equal to zero and attempt to solve:

Simplifying
3 + -5k + k2 = 0

Solving
3 + -5k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -5k + -3 + k2 = 0 + -3

Reorder the terms:
3 + -3 + -5k + k2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5k + k2 = 0 + -3
-5k + k2 = 0 + -3

Combine like terms: 0 + -3 = -3
-5k + k2 = -3

The k term is -5k.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5k + 6.25 + k2 = -3 + 6.25

Reorder the terms:
6.25 + -5k + k2 = -3 + 6.25

Combine like terms: -3 + 6.25 = 3.25
6.25 + -5k + k2 = 3.25

Factor a perfect square on the left side:
(k + -2.5)(k + -2.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(k + -2.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
k + -2.5 = 1.802775638

Simplifying
k + -2.5 = 1.802775638

Reorder the terms:
-2.5 + k = 1.802775638

Solving
-2.5 + k = 1.802775638

Solving for variable 'k'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + k = 1.802775638 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + k = 1.802775638 + 2.5
k = 1.802775638 + 2.5

Combine like terms: 1.802775638 + 2.5 = 4.302775638
k = 4.302775638

Simplifying
k = 4.302775638

Subproblem 2
k + -2.5 = -1.802775638

Simplifying
k + -2.5 = -1.802775638

Reorder the terms:
-2.5 + k = -1.802775638

Solving
-2.5 + k = -1.802775638

Solving for variable 'k'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + k = -1.802775638 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + k = -1.802775638 + 2.5
k = -1.802775638 + 2.5

Combine like terms: -1.802775638 + 2.5 = 0.697224362
k = 0.697224362

Simplifying
k = 0.697224362

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {4.302775638, 0.697224362}
Solution
k = {4.302775638, 0.697224362}