2k^2-12k=14

Solution for 2k^2-12k=14 equation:

Simplifying
2k2 + -12k = 14

Reorder the terms:
-12k + 2k2 = 14

Solving
-12k + 2k2 = 14

Solving for variable 'k'.

Reorder the terms:
-14 + -12k + 2k2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + -12k + 2k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -6k + k2) = 0

Factor a trinomial.
2((-1 + -1k)(7 + -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 '(7 + -1k)' equal to zero and attempt to solve:

Simplifying
7 + -1k = 0

Solving
7 + -1k = 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 + -1k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1k = 0 + -7
-1k = 0 + -7

Combine like terms: 0 + -7 = -7
-1k = -7

Divide each side by '-1'.
k = 7

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