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

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

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

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

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

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

Combine like terms: -1m + 6m = 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((-3 + -1m)(1 + -2m)) = 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 '(-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
Subproblem 3
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
Solution
m = {0, -3, 0.5}