21k^2+144k+108=0

Solution for 21k^2+144k+108=0 equation:

Simplifying
21k2 + 144k + 108 = 0

Reorder the terms:
108 + 144k + 21k2 = 0

Solving
108 + 144k + 21k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3'.
3(36 + 48k + 7k2) = 0

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

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(6 + 7k)' equal to zero and attempt to solve:

Simplifying
6 + 7k = 0

Solving
6 + 7k = 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 + 7k = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 7k = 0 + -6
7k = 0 + -6

Combine like terms: 0 + -6 = -6
7k = -6

Divide each side by '7'.
k = -0.8571428571

Simplifying
k = -0.8571428571
Solution
k = {-6, -0.8571428571}