8k^2+40k+50=0

Solution for 8k^2+40k+50=0 equation:

Simplifying
8k2 + 40k + 50 = 0

Reorder the terms:
50 + 40k + 8k2 = 0

Solving
50 + 40k + 8k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + 20k + 4k2) = 0

Factor a trinomial.
2((5 + 2k)(5 + 2k)) = 0

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

Simplifying
5 + 2k = 0

Solving
5 + 2k = 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 + 2k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2k = 0 + -5
2k = 0 + -5

Combine like terms: 0 + -5 = -5
2k = -5

Divide each side by '2'.
k = -2.5

Simplifying
k = -2.5
Subproblem 2
Set the factor '(5 + 2k)' equal to zero and attempt to solve:

Simplifying
5 + 2k = 0

Solving
5 + 2k = 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 + 2k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2k = 0 + -5
2k = 0 + -5

Combine like terms: 0 + -5 = -5
2k = -5

Divide each side by '2'.
k = -2.5

Simplifying
k = -2.5
Solution
k = {-2.5, -2.5}