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

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

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

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

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

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

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

Solving
-1 + 1m + 6m2 = 0

Solving for variable 'm'.

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

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

Simplifying
1 + -3m = 0

Solving
1 + -3m = 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 + -3m = 0 + -1

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

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

Divide each side by '-3'.
m = 0.3333333333

Simplifying
m = 0.3333333333
Solution
m = {-0.5, 0.3333333333}