(-3k^2)=2k+6

Solution for (-3k^2)=2k+6 equation:

Simplifying
(-3k2) = 2k + 6

Reorder the terms:
(-3k2) = 6 + 2k

Solving
(-3k2) = 6 + 2k

Solving for variable 'k'.

Reorder the terms:
-6 + -2k + (-3k2) = 6 + 2k + -6 + -2k

Reorder the terms:
-6 + -2k + (-3k2) = 6 + -6 + 2k + -2k

Combine like terms: 6 + -6 = 0
-6 + -2k + (-3k2) = 0 + 2k + -2k
-6 + -2k + (-3k2) = 2k + -2k

Combine like terms: 2k + -2k = 0
-6 + -2k + (-3k2) = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 2k + (3k2)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + 2k + (3k2))' equal to zero and attempt to solve:

Simplifying
6 + 2k + (3k2) = 0

Solving
6 + 2k + (3k2) = 0

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

Divide each side by '3'.
2 + 0.6666666667k + k2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 0.6666666667k + -2 + k2 = 0 + -2

Reorder the terms:
2 + -2 + 0.6666666667k + k2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 0.6666666667k + k2 = 0 + -2
0.6666666667k + k2 = 0 + -2

Combine like terms: 0 + -2 = -2
0.6666666667k + k2 = -2

The k term is 0.6666666667k.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667k + 0.1111111112 + k2 = -2 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667k + k2 = -2 + 0.1111111112

Combine like terms: -2 + 0.1111111112 = -1.8888888888
0.1111111112 + 0.6666666667k + k2 = -1.8888888888

Factor a perfect square on the left side:
((k) + 0.3333333334)((k) + 0.3333333334) = -1.8888888888

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.