3m^2+19m+6=0

Solution for 3m^2+19m+6=0 equation:

Simplifying
3m2 + 19m + 6 = 0

Reorder the terms:
6 + 19m + 3m2 = 0

Solving
6 + 19m + 3m2 = 0

Solving for variable 'm'.

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

Subproblem 1
Set the factor '(6 + m)' equal to zero and attempt to solve:

Simplifying
6 + m = 0

Solving
6 + m = 0

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

Add '-6' to each side of the equation.
6 + -6 + m = 0 + -6

Combine like terms: 6 + -6 = 0
0 + m = 0 + -6
m = 0 + -6

Combine like terms: 0 + -6 = -6
m = -6

Simplifying
m = -6
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 = {-6, -0.3333333333}