3k^2+39k+126=0

Solution for 3k^2+39k+126=0 equation:

Simplifying
3k2 + 39k + 126 = 0

Reorder the terms:
126 + 39k + 3k2 = 0

Solving
126 + 39k + 3k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3'.
3(42 + 13k + k2) = 0

Factor a trinomial.
3((7 + k)(6 + k)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(7 + k)' equal to zero and attempt to solve:

Simplifying
7 + k = 0

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

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

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

Simplifying
k = -7
Subproblem 2
Set the factor '(6 + k)' equal to zero and attempt to solve:

Simplifying
6 + k = 0

Solving
6 + k = 0

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

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

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

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

Simplifying
k = -6
Solution
k = {-7, -6}