6k^4+29k^3+30k^2=0

Solution for 6k^4+29k^3+30k^2=0 equation:

Simplifying
6k4 + 29k3 + 30k2 = 0

Reorder the terms:
30k2 + 29k3 + 6k4 = 0

Solving
30k2 + 29k3 + 6k4 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), 'k2'.
k2(30 + 29k + 6k2) = 0

Factor a trinomial.
k2((10 + 3k)(3 + 2k)) = 0

Subproblem 1
Set the factor 'k2' equal to zero and attempt to solve:

Simplifying
k2 = 0

Solving
k2 = 0

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

Simplifying
k2 = 0

Take the square root of each side:
k = {0}
Subproblem 2
Set the factor '(10 + 3k)' equal to zero and attempt to solve:

Simplifying
10 + 3k = 0

Solving
10 + 3k = 0

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

Add '-10' to each side of the equation.
10 + -10 + 3k = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 3k = 0 + -10
3k = 0 + -10

Combine like terms: 0 + -10 = -10
3k = -10

Divide each side by '3'.
k = -3.333333333

Simplifying
k = -3.333333333
Subproblem 3
Set the factor '(3 + 2k)' equal to zero and attempt to solve:

Simplifying
3 + 2k = 0

Solving
3 + 2k = 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 + 2k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2k = 0 + -3
2k = 0 + -3

Combine like terms: 0 + -3 = -3
2k = -3

Divide each side by '2'.
k = -1.5

Simplifying
k = -1.5
Solution
k = {0, -3.333333333, -1.5}