-4k^2-8k=3-k^2

Solution for -4k^2-8k=3-k^2 equation:

Simplifying
-4k2 + -8k = 3 + -1k2

Reorder the terms:
-8k + -4k2 = 3 + -1k2

Solving
-8k + -4k2 = 3 + -1k2

Solving for variable 'k'.

Reorder the terms:
-3 + -8k + -4k2 + k2 = 3 + -1k2 + -3 + k2

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

Reorder the terms:
-3 + -8k + -3k2 = 3 + -3 + -1k2 + k2

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 8k + 3k2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 8k + 3k2)' equal to zero and attempt to solve:

Simplifying
3 + 8k + 3k2 = 0

Solving
3 + 8k + 3k2 = 0

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

Divide each side by '3'.
1 + 2.666666667k + k2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 2.666666667k + -1 + k2 = 0 + -1

Reorder the terms:
1 + -1 + 2.666666667k + k2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2.666666667k + k2 = 0 + -1
2.666666667k + k2 = 0 + -1

Combine like terms: 0 + -1 = -1
2.666666667k + k2 = -1

The k term is 2.666666667k.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667k + 1.777777780 + k2 = -1 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667k + k2 = -1 + 1.777777780

Combine like terms: -1 + 1.777777780 = 0.77777778
1.777777780 + 2.666666667k + k2 = 0.77777778

Factor a perfect square on the left side:
(k + 1.333333334)(k + 1.333333334) = 0.77777778

Calculate the square root of the right side: 0.881917105

Break this problem into two subproblems by setting 
(k + 1.333333334) equal to 0.881917105 and -0.881917105.

Subproblem 1
k + 1.333333334 = 0.881917105

Simplifying
k + 1.333333334 = 0.881917105

Reorder the terms:
1.333333334 + k = 0.881917105

Solving
1.333333334 + k = 0.881917105

Solving for variable 'k'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + k = 0.881917105 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + k = 0.881917105 + -1.333333334
k = 0.881917105 + -1.333333334

Combine like terms: 0.881917105 + -1.333333334 = -0.451416229
k = -0.451416229

Simplifying
k = -0.451416229

Subproblem 2
k + 1.333333334 = -0.881917105

Simplifying
k + 1.333333334 = -0.881917105

Reorder the terms:
1.333333334 + k = -0.881917105

Solving
1.333333334 + k = -0.881917105

Solving for variable 'k'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + k = -0.881917105 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + k = -0.881917105 + -1.333333334
k = -0.881917105 + -1.333333334

Combine like terms: -0.881917105 + -1.333333334 = -2.215250439
k = -2.215250439

Simplifying
k = -2.215250439

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {-0.451416229, -2.215250439}
Solution
k = {-0.451416229, -2.215250439}