20k^2+106k+72=0

Solution for 20k^2+106k+72=0 equation:

Simplifying
20k2 + 106k + 72 = 0

Reorder the terms:
72 + 106k + 20k2 = 0

Solving
72 + 106k + 20k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(36 + 53k + 10k2) = 0

Factor a trinomial.
2((9 + 2k)(4 + 5k)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(9 + 2k)' equal to zero and attempt to solve:

Simplifying
9 + 2k = 0

Solving
9 + 2k = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2k = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2k = 0 + -9
2k = 0 + -9

Combine like terms: 0 + -9 = -9
2k = -9

Divide each side by '2'.
k = -4.5

Simplifying
k = -4.5
Subproblem 2
Set the factor '(4 + 5k)' equal to zero and attempt to solve:

Simplifying
4 + 5k = 0

Solving
4 + 5k = 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 + 5k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5k = 0 + -4
5k = 0 + -4

Combine like terms: 0 + -4 = -4
5k = -4

Divide each side by '5'.
k = -0.8

Simplifying
k = -0.8
Solution
k = {-4.5, -0.8}