12k^2+2k-10=0

Solution for 12k^2+2k-10=0 equation:

Simplifying
12k2 + 2k + -10 = 0

Reorder the terms:
-10 + 2k + 12k2 = 0

Solving
-10 + 2k + 12k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + k + 6k2) = 0

Factor a trinomial.
2((-1 + -1k)(5 + -6k)) = 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 '(5 + -6k)' equal to zero and attempt to solve:

Simplifying
5 + -6k = 0

Solving
5 + -6k = 0

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

Add '-5' to each side of the equation.
5 + -5 + -6k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6k = 0 + -5
-6k = 0 + -5

Combine like terms: 0 + -5 = -5
-6k = -5

Divide each side by '-6'.
k = 0.8333333333

Simplifying
k = 0.8333333333
Solution
k = {-1, 0.8333333333}