77k^2+91k+14=0

Solution for 77k^2+91k+14=0 equation:

Simplifying
77k2 + 91k + 14 = 0

Reorder the terms:
14 + 91k + 77k2 = 0

Solving
14 + 91k + 77k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '7'.
7(2 + 13k + 11k2) = 0

Factor a trinomial.
7((1 + k)(2 + 11k)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(1 + k)' equal to zero and attempt to solve:

Simplifying
1 + k = 0

Solving
1 + k = 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 + k = 0 + -1

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

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

Simplifying
k = -1
Subproblem 2
Set the factor '(2 + 11k)' equal to zero and attempt to solve:

Simplifying
2 + 11k = 0

Solving
2 + 11k = 0

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

Add '-2' to each side of the equation.
2 + -2 + 11k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 11k = 0 + -2
11k = 0 + -2

Combine like terms: 0 + -2 = -2
11k = -2

Divide each side by '11'.
k = -0.1818181818

Simplifying
k = -0.1818181818
Solution
k = {-1, -0.1818181818}