k^2-8k+20=k

Solution for k^2-8k+20=k equation:

Simplifying
k2 + -8k + 20 = k

Reorder the terms:
20 + -8k + k2 = k

Solving
20 + -8k + k2 = k

Solving for variable 'k'.

Reorder the terms:
20 + -8k + -1k + k2 = k + -1k

Combine like terms: -8k + -1k = -9k
20 + -9k + k2 = k + -1k

Combine like terms: k + -1k = 0
20 + -9k + k2 = 0

Factor a trinomial.
(4 + -1k)(5 + -1k) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -1k)' equal to zero and attempt to solve:

Simplifying
5 + -1k = 0

Solving
5 + -1k = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1k = 0 + -5
-1k = 0 + -5

Combine like terms: 0 + -5 = -5
-1k = -5

Divide each side by '-1'.
k = 5

Simplifying
k = 5
Solution
k = {4, 5}