-5k-6k^2-12k+10=0

Solution for -5k-6k^2-12k+10=0 equation:

Simplifying
-5k + -6k2 + -12k + 10 = 0

Reorder the terms:
10 + -5k + -12k + -6k2 = 0

Combine like terms: -5k + -12k = -17k
10 + -17k + -6k2 = 0

Solving
10 + -17k + -6k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(1 + -2k)(10 + 3k) = 0

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

Simplifying
1 + -2k = 0

Solving
1 + -2k = 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 + -2k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2k = 0 + -1
-2k = 0 + -1

Combine like terms: 0 + -1 = -1
-2k = -1

Divide each side by '-2'.
k = 0.5

Simplifying
k = 0.5
Subproblem 2
Set the factor '(10 + 3k)' equal to zero and attempt to solve:

Simplifying
10 + 3k = 0

Solving
10 + 3k = 0

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

Add '-10' to each side of the equation.
10 + -10 + 3k = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 3k = 0 + -10
3k = 0 + -10

Combine like terms: 0 + -10 = -10
3k = -10

Divide each side by '3'.
k = -3.333333333

Simplifying
k = -3.333333333
Solution
k = {0.5, -3.333333333}