0=-k^2+2k+8

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Solution for 0=-k^2+2k+8 equation: 


Simplifying
0 = -1k2 + 2k + 8

Reorder the terms:
0 = 8 + 2k + -1k2

Solving
0 = 8 + 2k + -1k2

Solving for variable 'k'.

Combine like terms: 0 + -8 = -8
-8 + -2k + k2 = 8 + 2k + -1k2 + -8 + -2k + k2

Reorder the terms:
-8 + -2k + k2 = 8 + -8 + 2k + -2k + -1k2 + k2

Combine like terms: 8 + -8 = 0
-8 + -2k + k2 = 0 + 2k + -2k + -1k2 + k2
-8 + -2k + k2 = 2k + -2k + -1k2 + k2

Combine like terms: 2k + -2k = 0
-8 + -2k + k2 = 0 + -1k2 + k2
-8 + -2k + k2 = -1k2 + k2

Combine like terms: -1k2 + k2 = 0
-8 + -2k + k2 = 0

Factor a trinomial.
(-2 + -1k)(4 + -1k) = 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 '(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 = {-2, 4}

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