2m=6m^2-4

Solution for 2m=6m^2-4 equation:

Simplifying
2m = 6m2 + -4

Reorder the terms:
2m = -4 + 6m2

Solving
2m = -4 + 6m2

Solving for variable 'm'.

Reorder the terms:
4 + 2m + -6m2 = -4 + 6m2 + 4 + -6m2

Reorder the terms:
4 + 2m + -6m2 = -4 + 4 + 6m2 + -6m2

Combine like terms: -4 + 4 = 0
4 + 2m + -6m2 = 0 + 6m2 + -6m2
4 + 2m + -6m2 = 6m2 + -6m2

Combine like terms: 6m2 + -6m2 = 0
4 + 2m + -6m2 = 0

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

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

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

Simplifying
1 + -1m = 0

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

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

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

Divide each side by '-1'.
m = 1

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

Simplifying
2 + 3m = 0

Solving
2 + 3m = 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 + 3m = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3m = 0 + -2
3m = 0 + -2

Combine like terms: 0 + -2 = -2
3m = -2

Divide each side by '3'.
m = -0.6666666667

Simplifying
m = -0.6666666667
Solution
m = {1, -0.6666666667}