k^2=-2k+24

Solution for k^2=-2k+24 equation:

Simplifying
k2 = -2k + 24

Reorder the terms:
k2 = 24 + -2k

Solving
k2 = 24 + -2k

Solving for variable 'k'.

Reorder the terms:
-24 + 2k + k2 = 24 + -2k + -24 + 2k

Reorder the terms:
-24 + 2k + k2 = 24 + -24 + -2k + 2k

Combine like terms: 24 + -24 = 0
-24 + 2k + k2 = 0 + -2k + 2k
-24 + 2k + k2 = -2k + 2k

Combine like terms: -2k + 2k = 0
-24 + 2k + k2 = 0

Factor a trinomial.
(-6 + -1k)(4 + -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 '(4 + -1k)' equal to zero and attempt to solve:

Simplifying
4 + -1k = 0

Solving
4 + -1k = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1k = 0 + -4
-1k = 0 + -4

Combine like terms: 0 + -4 = -4
-1k = -4

Divide each side by '-1'.
k = 4

Simplifying
k = 4
Solution
k = {-6, 4}