8m^2-2m-6=0

Solution for 8m^2-2m-6=0 equation:

Simplifying
8m2 + -2m + -6 = 0

Reorder the terms:
-6 + -2m + 8m2 = 0

Solving
-6 + -2m + 8m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -1m + 4m2) = 0

Factor a trinomial.
2((-3 + -4m)(1 + -1m)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -4m)' equal to zero and attempt to solve:

Simplifying
-3 + -4m = 0

Solving
-3 + -4m = 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 + -4m = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4m = 0 + 3
-4m = 0 + 3

Combine like terms: 0 + 3 = 3
-4m = 3

Divide each side by '-4'.
m = -0.75

Simplifying
m = -0.75
Subproblem 2
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
Solution
m = {-0.75, 1}