m^2(3m+1)=2m

Solution for m^2(3m+1)=2m equation:

Simplifying
m2(3m + 1) = 2m

Reorder the terms:
m2(1 + 3m) = 2m
(1 * m2 + 3m * m2) = 2m
(1m2 + 3m3) = 2m

Solving
1m2 + 3m3 = 2m

Solving for variable 'm'.

Reorder the terms:
-2m + 1m2 + 3m3 = 2m + -2m

Combine like terms: 2m + -2m = 0
-2m + 1m2 + 3m3 = 0

Factor out the Greatest Common Factor (GCF), 'm'.
m(-2 + m + 3m2) = 0

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

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

Simplifying
m = 0

Solving
m = 0

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

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

Simplifying
-1 + -1m = 0

Solving
-1 + -1m = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1m = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1m = 0 + 1
-1m = 0 + 1

Combine like terms: 0 + 1 = 1
-1m = 1

Divide each side by '-1'.
m = -1

Simplifying
m = -1
Subproblem 3
Set the factor '(2 + -3m)' equal to zero and attempt to solve:

Simplifying
2 + -3m = 0

Solving
2 + -3m = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3m = 0 + -2

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

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

Divide each side by '-3'.
m = 0.6666666667

Simplifying
m = 0.6666666667
Solution
m = {0, -1, 0.6666666667}