2k^2-14k=16

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

Simplifying
2k2 + -14k = 16

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

Solving
-14k + 2k2 = 16

Solving for variable 'k'.

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

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

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

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

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

Simplifying
8 + -1k = 0

Solving
8 + -1k = 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 + -1k = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1k = 0 + -8
-1k = 0 + -8

Combine like terms: 0 + -8 = -8
-1k = -8

Divide each side by '-1'.
k = 8

Simplifying
k = 8
Solution
k = {-1, 8}