8k^3=2k^2+3k

Solution for 8k^3=2k^2+3k equation:

Simplifying
8k3 = 2k2 + 3k

Reorder the terms:
8k3 = 3k + 2k2

Solving
8k3 = 3k + 2k2

Solving for variable 'k'.

Reorder the terms:
-3k + -2k2 + 8k3 = 3k + 2k2 + -3k + -2k2

Reorder the terms:
-3k + -2k2 + 8k3 = 3k + -3k + 2k2 + -2k2

Combine like terms: 3k + -3k = 0
-3k + -2k2 + 8k3 = 0 + 2k2 + -2k2
-3k + -2k2 + 8k3 = 2k2 + -2k2

Combine like terms: 2k2 + -2k2 = 0
-3k + -2k2 + 8k3 = 0

Factor out the Greatest Common Factor (GCF), 'k'.
k(-3 + -2k + 8k2) = 0

Factor a trinomial.
k((-1 + -2k)(3 + -4k)) = 0

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

Simplifying
k = 0

Solving
k = 0

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

Simplifying
k = 0
Subproblem 2
Set the factor '(-1 + -2k)' equal to zero and attempt to solve:

Simplifying
-1 + -2k = 0

Solving
-1 + -2k = 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 + -2k = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2k = 0 + 1
-2k = 0 + 1

Combine like terms: 0 + 1 = 1
-2k = 1

Divide each side by '-2'.
k = -0.5

Simplifying
k = -0.5
Subproblem 3
Set the factor '(3 + -4k)' equal to zero and attempt to solve:

Simplifying
3 + -4k = 0

Solving
3 + -4k = 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 + -4k = 0 + -3

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

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

Divide each side by '-4'.
k = 0.75

Simplifying
k = 0.75
Solution
k = {0, -0.5, 0.75}