4m^2x^2-2mx-2=0

Solution for 4m^2x^2-2mx-2=0 equation:

Simplifying
4m2x2 + -2mx + -2 = 0

Reorder the terms:
-2 + -2mx + 4m2x2 = 0

Solving
-2 + -2mx + 4m2x2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -1mx + 2m2x2) = 0

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

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

Simplifying
-1 + -2mx = 0

Solving
-1 + -2mx = 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 + -2mx = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2mx = 0 + 1
-2mx = 0 + 1

Combine like terms: 0 + 1 = 1
-2mx = 1

Divide each side by '-2x'.
m = -0.5x-1

Simplifying
m = -0.5x-1
Subproblem 2
Set the factor '(1 + -1mx)' equal to zero and attempt to solve:

Simplifying
1 + -1mx = 0

Solving
1 + -1mx = 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 + -1mx = 0 + -1

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

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

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

Simplifying
m = x-1
Solution
m = {-0.5x-1, x-1}