36k^4-48k^3-20k^2=0

Solution for 36k^4-48k^3-20k^2=0 equation:

Simplifying
36k4 + -48k3 + -20k2 = 0

Reorder the terms:
-20k2 + -48k3 + 36k4 = 0

Solving
-20k2 + -48k3 + 36k4 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '4k2'.
4k2(-5 + -12k + 9k2) = 0

Factor a trinomial.
4k2((-1 + -3k)(5 + -3k)) = 0

Ignore the factor 4.
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 '(-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
Subproblem 3
Set the factor '(5 + -3k)' equal to zero and attempt to solve:

Simplifying
5 + -3k = 0

Solving
5 + -3k = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3k = 0 + -5
-3k = 0 + -5

Combine like terms: 0 + -5 = -5
-3k = -5

Divide each side by '-3'.
k = 1.666666667

Simplifying
k = 1.666666667
Solution
k = {0, -0.3333333333, 1.666666667}