0=k*k+k-6

Solution for 0=k*k+k-6 equation:

Simplifying
0 = k * k + k + -6

Multiply k * k
0 = k2 + k + -6

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

Solving
0 = -6 + k + k2

Solving for variable 'k'.

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

Reorder the terms:
6 + -1k + -1k2 = -6 + 6 + k + -1k + k2 + -1k2

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

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

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

Factor a trinomial.
(2 + -1k)(3 + k) = 0

Subproblem 1
Set the factor '(2 + -1k)' equal to zero and attempt to solve:

Simplifying
2 + -1k = 0

Solving
2 + -1k = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1k = 0 + -2
-1k = 0 + -2

Combine like terms: 0 + -2 = -2
-1k = -2

Divide each side by '-1'.
k = 2

Simplifying
k = 2
Subproblem 2
Set the factor '(3 + k)' equal to zero and attempt to solve:

Simplifying
3 + k = 0

Solving
3 + k = 0

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 = 0 + -3

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

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

Simplifying
k = -3
Solution
k = {2, -3}