k+1(k^2+5k+6)=0

Solution for k+1(k^2+5k+6)=0 equation:

Simplifying
k + 1(k2 + 5k + 6) = 0

Reorder the terms:
k + 1(6 + 5k + k2) = 0
k + (6 * 1 + 5k * 1 + k2 * 1) = 0
k + (6 + 5k + 1k2) = 0

Reorder the terms:
6 + k + 5k + 1k2 = 0

Combine like terms: k + 5k = 6k
6 + 6k + 1k2 = 0

Solving
6 + 6k + 1k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 6k + -6 + k2 = 0 + -6

Reorder the terms:
6 + -6 + 6k + k2 = 0 + -6

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

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

The k term is 6k.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6k + 9 + k2 = -6 + 9

Reorder the terms:
9 + 6k + k2 = -6 + 9

Combine like terms: -6 + 9 = 3
9 + 6k + k2 = 3

Factor a perfect square on the left side:
(k + 3)(k + 3) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(k + 3) equal to 1.732050808 and -1.732050808.

Subproblem 1
k + 3 = 1.732050808

Simplifying
k + 3 = 1.732050808

Reorder the terms:
3 + k = 1.732050808

Solving
3 + k = 1.732050808

Solving for variable 'k'.

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

Add '-3' to each side of the equation.
3 + -3 + k = 1.732050808 + -3

Combine like terms: 3 + -3 = 0
0 + k = 1.732050808 + -3
k = 1.732050808 + -3

Combine like terms: 1.732050808 + -3 = -1.267949192
k = -1.267949192

Simplifying
k = -1.267949192

Subproblem 2
k + 3 = -1.732050808

Simplifying
k + 3 = -1.732050808

Reorder the terms:
3 + k = -1.732050808

Solving
3 + k = -1.732050808

Solving for variable 'k'.

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

Add '-3' to each side of the equation.
3 + -3 + k = -1.732050808 + -3

Combine like terms: 3 + -3 = 0
0 + k = -1.732050808 + -3
k = -1.732050808 + -3

Combine like terms: -1.732050808 + -3 = -4.732050808
k = -4.732050808

Simplifying
k = -4.732050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {-1.267949192, -4.732050808}