6m^2+14m+4=0

Solution for 6m^2+14m+4=0 equation:

Simplifying
6m2 + 14m + 4 = 0

Reorder the terms:
4 + 14m + 6m2 = 0

Solving
4 + 14m + 6m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 7m + 3m2) = 0

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

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

Simplifying
2 + m = 0

Solving
2 + m = 0

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

Add '-2' to each side of the equation.
2 + -2 + m = 0 + -2

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

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

Simplifying
m = -2
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 = {-2, -0.3333333333}