3k^3+3k=10k^2

Solution for 3k^3+3k=10k^2 equation:

Simplifying
3k3 + 3k = 10k2

Reorder the terms:
3k + 3k3 = 10k2

Solving
3k + 3k3 = 10k2

Solving for variable 'k'.

Reorder the terms:
3k + -10k2 + 3k3 = 10k2 + -10k2

Combine like terms: 10k2 + -10k2 = 0
3k + -10k2 + 3k3 = 0

Factor out the Greatest Common Factor (GCF), 'k'.
k(3 + -10k + 3k2) = 0

Factor a trinomial.
k((1 + -3k)(3 + -1k)) = 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 + -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 '(3 + -1k)' equal to zero and attempt to solve:

Simplifying
3 + -1k = 0

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

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

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

Divide each side by '-1'.
k = 3

Simplifying
k = 3
Solution
k = {0, 0.3333333333, 3}