14k^2+2k-16=0

Solution for 14k^2+2k-16=0 equation:

Simplifying
14k2 + 2k + -16 = 0

Reorder the terms:
-16 + 2k + 14k2 = 0

Solving
-16 + 2k + 14k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + k + 7k2) = 0

Factor a trinomial.
2((-8 + -7k)(1 + -1k)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -7k)' equal to zero and attempt to solve:

Simplifying
-8 + -7k = 0

Solving
-8 + -7k = 0

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

Add '8' to each side of the equation.
-8 + 8 + -7k = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -7k = 0 + 8
-7k = 0 + 8

Combine like terms: 0 + 8 = 8
-7k = 8

Divide each side by '-7'.
k = -1.142857143

Simplifying
k = -1.142857143
Subproblem 2
Set the factor '(1 + -1k)' equal to zero and attempt to solve:

Simplifying
1 + -1k = 0

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

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

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

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

Simplifying
k = 1
Solution
k = {-1.142857143, 1}