k^2=-3k+18

Solution for k^2=-3k+18 equation:

Simplifying
k2 = -3k + 18

Reorder the terms:
k2 = 18 + -3k

Solving
k2 = 18 + -3k

Solving for variable 'k'.

Reorder the terms:
-18 + 3k + k2 = 18 + -3k + -18 + 3k

Reorder the terms:
-18 + 3k + k2 = 18 + -18 + -3k + 3k

Combine like terms: 18 + -18 = 0
-18 + 3k + k2 = 0 + -3k + 3k
-18 + 3k + k2 = -3k + 3k

Combine like terms: -3k + 3k = 0
-18 + 3k + k2 = 0

Factor a trinomial.
(-6 + -1k)(3 + -1k) = 0

Subproblem 1
Set the factor '(-6 + -1k)' equal to zero and attempt to solve:

Simplifying
-6 + -1k = 0

Solving
-6 + -1k = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1k = 0 + 6

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

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

Divide each side by '-1'.
k = -6

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

Simplifying
3 + -1k = 0

Solving
3 + -1k = 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 + -1k = 0 + -3

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

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

Divide each side by '-1'.
k = 3

Simplifying
k = 3
Solution
k = {-6, 3}