k^2-20k+51=0

Solution for k^2-20k+51=0 equation:

Simplifying
k2 + -20k + 51 = 0

Reorder the terms:
51 + -20k + k2 = 0

Solving
51 + -20k + k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(3 + -1k)(17 + -1k) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(17 + -1k)' equal to zero and attempt to solve:

Simplifying
17 + -1k = 0

Solving
17 + -1k = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1k = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1k = 0 + -17
-1k = 0 + -17

Combine like terms: 0 + -17 = -17
-1k = -17

Divide each side by '-1'.
k = 17

Simplifying
k = 17
Solution
k = {3, 17}