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

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

Simplifying
-3(2m2 + 3m + 1) = 0

Reorder the terms:
-3(1 + 3m + 2m2) = 0
(1 * -3 + 3m * -3 + 2m2 * -3) = 0
(-3 + -9m + -6m2) = 0

Solving
-3 + -9m + -6m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '-3'.
-3(1 + 3m + 2m2) = 0

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

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

Simplifying
1 + m = 0

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

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

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

Simplifying
m = -1
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
Solution
m = {-1, -0.5}