2k^2=-14-16k

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

Simplifying
2k2 = -14 + -16k

Solving
2k2 = -14 + -16k

Solving for variable 'k'.

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

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

Combine like terms: -14 + 14 = 0
14 + 16k + 2k2 = 0 + -16k + 16k
14 + 16k + 2k2 = -16k + 16k

Combine like terms: -16k + 16k = 0
14 + 16k + 2k2 = 0

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

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

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

Simplifying
7 + k = 0

Solving
7 + k = 0

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

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

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

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

Simplifying
k = -7
Subproblem 2
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
Solution
k = {-7, -1}