51+20k+k^2=0

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

Simplifying
51 + 20k + k2 = 0

Solving
51 + 20k + k2 = 0

Solving for variable 'k'.

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

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

Simplifying
17 + k = 0

Solving
17 + k = 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 + k = 0 + -17

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

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

Simplifying
k = -17
Subproblem 2
Set the factor '(3 + k)' equal to zero and attempt to solve:

Simplifying
3 + k = 0

Solving
3 + k = 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 + k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + k = 0 + -3
k = 0 + -3

Combine like terms: 0 + -3 = -3
k = -3

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