(k^2-24k+80)=0

Solution for (k^2-24k+80)=0 equation:

Simplifying
(k2 + -24k + 80) = 0

Reorder the terms:
(80 + -24k + k2) = 0

Remove parenthesis around (80 + -24k + k2)
80 + -24k + k2 = 0

Solving
80 + -24k + k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(4 + -1k)(20 + -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 '(20 + -1k)' equal to zero and attempt to solve:

Simplifying
20 + -1k = 0

Solving
20 + -1k = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1k = 0 + -20

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

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

Divide each side by '-1'.
k = 20

Simplifying
k = 20
Solution
k = {4, 20}