27k^2+45k+12=0

Solution for 27k^2+45k+12=0 equation:

Simplifying
27k2 + 45k + 12 = 0

Reorder the terms:
12 + 45k + 27k2 = 0

Solving
12 + 45k + 27k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + 15k + 9k2) = 0

Factor a trinomial.
3((4 + 3k)(1 + 3k)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(4 + 3k)' equal to zero and attempt to solve:

Simplifying
4 + 3k = 0

Solving
4 + 3k = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3k = 0 + -4
3k = 0 + -4

Combine like terms: 0 + -4 = -4
3k = -4

Divide each side by '3'.
k = -1.333333333

Simplifying
k = -1.333333333
Subproblem 2
Set the factor '(1 + 3k)' equal to zero and attempt to solve:

Simplifying
1 + 3k = 0

Solving
1 + 3k = 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 + 3k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3k = 0 + -1
3k = 0 + -1

Combine like terms: 0 + -1 = -1
3k = -1

Divide each side by '3'.
k = -0.3333333333

Simplifying
k = -0.3333333333
Solution
k = {-1.333333333, -0.3333333333}