2(4m+1)(m-1)=0

Solution for 2(4m+1)(m-1)=0 equation:

Simplifying
2(4m + 1)(m + -1) = 0

Reorder the terms:
2(1 + 4m)(m + -1) = 0

Reorder the terms:
2(1 + 4m)(-1 + m) = 0

Multiply (1 + 4m) * (-1 + m)
2(1(-1 + m) + 4m * (-1 + m)) = 0
2((-1 * 1 + m * 1) + 4m * (-1 + m)) = 0
2((-1 + 1m) + 4m * (-1 + m)) = 0
2(-1 + 1m + (-1 * 4m + m * 4m)) = 0
2(-1 + 1m + (-4m + 4m2)) = 0

Combine like terms: 1m + -4m = -3m
2(-1 + -3m + 4m2) = 0
(-1 * 2 + -3m * 2 + 4m2 * 2) = 0
(-2 + -6m + 8m2) = 0

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

Solving for variable 'm'.

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

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

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

Simplifying
-1 + -4m = 0

Solving
-1 + -4m = 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 + -4m = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4m = 0 + 1
-4m = 0 + 1

Combine like terms: 0 + 1 = 1
-4m = 1

Divide each side by '-4'.
m = -0.25

Simplifying
m = -0.25
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 = {-0.25, 1}