88k^2+204k+80=0

Solution for 88k^2+204k+80=0 equation:

Simplifying
88k2 + 204k + 80 = 0

Reorder the terms:
80 + 204k + 88k2 = 0

Solving
80 + 204k + 88k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '4'.
4(20 + 51k + 22k2) = 0

Factor a trinomial.
4((20 + 11k)(1 + 2k)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(20 + 11k)' equal to zero and attempt to solve:

Simplifying
20 + 11k = 0

Solving
20 + 11k = 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 + 11k = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 11k = 0 + -20
11k = 0 + -20

Combine like terms: 0 + -20 = -20
11k = -20

Divide each side by '11'.
k = -1.818181818

Simplifying
k = -1.818181818
Subproblem 2
Set the factor '(1 + 2k)' equal to zero and attempt to solve:

Simplifying
1 + 2k = 0

Solving
1 + 2k = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2k = 0 + -1
2k = 0 + -1

Combine like terms: 0 + -1 = -1
2k = -1

Divide each side by '2'.
k = -0.5

Simplifying
k = -0.5
Solution
k = {-1.818181818, -0.5}