6k^2+12k-15=-10

Solution for 6k^2+12k-15=-10 equation:

Simplifying
6k2 + 12k + -15 = -10

Reorder the terms:
-15 + 12k + 6k2 = -10

Solving
-15 + 12k + 6k2 = -10

Solving for variable 'k'.

Reorder the terms:
-15 + 10 + 12k + 6k2 = -10 + 10

Combine like terms: -15 + 10 = -5
-5 + 12k + 6k2 = -10 + 10

Combine like terms: -10 + 10 = 0
-5 + 12k + 6k2 = 0

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

Divide each side by '6'.
-0.8333333333 + 2k + k2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + 2k + 0.8333333333 + k2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + 2k + k2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + 2k + k2 = 0 + 0.8333333333
2k + k2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
2k + k2 = 0.8333333333

The k term is 2k.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2k + 1 + k2 = 0.8333333333 + 1

Reorder the terms:
1 + 2k + k2 = 0.8333333333 + 1

Combine like terms: 0.8333333333 + 1 = 1.8333333333
1 + 2k + k2 = 1.8333333333

Factor a perfect square on the left side:
(k + 1)(k + 1) = 1.8333333333

Calculate the square root of the right side: 1.354006401

Break this problem into two subproblems by setting 
(k + 1) equal to 1.354006401 and -1.354006401.

Subproblem 1
k + 1 = 1.354006401

Simplifying
k + 1 = 1.354006401

Reorder the terms:
1 + k = 1.354006401

Solving
1 + k = 1.354006401

Solving for variable 'k'.

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

Add '-1' to each side of the equation.
1 + -1 + k = 1.354006401 + -1

Combine like terms: 1 + -1 = 0
0 + k = 1.354006401 + -1
k = 1.354006401 + -1

Combine like terms: 1.354006401 + -1 = 0.354006401
k = 0.354006401

Simplifying
k = 0.354006401

Subproblem 2
k + 1 = -1.354006401

Simplifying
k + 1 = -1.354006401

Reorder the terms:
1 + k = -1.354006401

Solving
1 + k = -1.354006401

Solving for variable 'k'.

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

Add '-1' to each side of the equation.
1 + -1 + k = -1.354006401 + -1

Combine like terms: 1 + -1 = 0
0 + k = -1.354006401 + -1
k = -1.354006401 + -1

Combine like terms: -1.354006401 + -1 = -2.354006401
k = -2.354006401

Simplifying
k = -2.354006401

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.354006401, -2.354006401}