12k^2+42k+30=0

Solution for 12k^2+42k+30=0 equation:

Simplifying
12k2 + 42k + 30 = 0

Reorder the terms:
30 + 42k + 12k2 = 0

Solving
30 + 42k + 12k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '6'.
6(5 + 7k + 2k2) = 0

Factor a trinomial.
6((5 + 2k)(1 + k)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(5 + 2k)' equal to zero and attempt to solve:

Simplifying
5 + 2k = 0

Solving
5 + 2k = 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 + 2k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2k = 0 + -5
2k = 0 + -5

Combine like terms: 0 + -5 = -5
2k = -5

Divide each side by '2'.
k = -2.5

Simplifying
k = -2.5
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 = {-2.5, -1}