32m^2-4m-6=0

Solution for 32m^2-4m-6=0 equation:

Simplifying
32m2 + -4m + -6 = 0

Reorder the terms:
-6 + -4m + 32m2 = 0

Solving
-6 + -4m + 32m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -2m + 16m2) = 0

Factor a trinomial.
2((-3 + -8m)(1 + -2m)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -8m)' equal to zero and attempt to solve:

Simplifying
-3 + -8m = 0

Solving
-3 + -8m = 0

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

Add '3' to each side of the equation.
-3 + 3 + -8m = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -8m = 0 + 3
-8m = 0 + 3

Combine like terms: 0 + 3 = 3
-8m = 3

Divide each side by '-8'.
m = -0.375

Simplifying
m = -0.375
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 = {-0.375, 0.5}