2k^2+10k=-12

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

Simplifying
2k2 + 10k = -12

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

Solving
10k + 2k2 = -12

Solving for variable 'k'.

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

Combine like terms: -12 + 12 = 0
12 + 10k + 2k2 = 0

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

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

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + k)' equal to zero and attempt to solve:

Simplifying
3 + k = 0

Solving
3 + k = 0

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

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

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

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

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

Simplifying
2 + k = 0

Solving
2 + k = 0

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

Add '-2' to each side of the equation.
2 + -2 + k = 0 + -2

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

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

Simplifying
k = -2
Solution
k = {-3, -2}