m(m-3)(2m+1)=0

Solution for m(m-3)(2m+1)=0 equation:

Simplifying
m(m + -3)(2m + 1) = 0

Reorder the terms:
m(-3 + m)(2m + 1) = 0

Reorder the terms:
m(-3 + m)(1 + 2m) = 0

Multiply (-3 + m) * (1 + 2m)
m(-3(1 + 2m) + m(1 + 2m)) = 0
m((1 * -3 + 2m * -3) + m(1 + 2m)) = 0
m((-3 + -6m) + m(1 + 2m)) = 0
m(-3 + -6m + (1 * m + 2m * m)) = 0
m(-3 + -6m + (1m + 2m2)) = 0

Combine like terms: -6m + 1m = -5m
m(-3 + -5m + 2m2) = 0
(-3 * m + -5m * m + 2m2 * m) = 0
(-3m + -5m2 + 2m3) = 0

Solving
-3m + -5m2 + 2m3 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), 'm'.
m(-3 + -5m + 2m2) = 0

Factor a trinomial.
m((-1 + -2m)(3 + -1m)) = 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 + -2m)' equal to zero and attempt to solve:

Simplifying
-1 + -2m = 0

Solving
-1 + -2m = 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 + -2m = 0 + 1

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

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

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

Simplifying
m = -0.5
Subproblem 3
Set the factor '(3 + -1m)' equal to zero and attempt to solve:

Simplifying
3 + -1m = 0

Solving
3 + -1m = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1m = 0 + -3

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

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

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

Simplifying
m = 3
Solution
m = {0, -0.5, 3}