(4m-3)(4m+1)=0

Solution for (4m-3)(4m+1)=0 equation:

Simplifying
(4m + -3)(4m + 1) = 0

Reorder the terms:
(-3 + 4m)(4m + 1) = 0

Reorder the terms:
(-3 + 4m)(1 + 4m) = 0

Multiply (-3 + 4m) * (1 + 4m)
(-3(1 + 4m) + 4m * (1 + 4m)) = 0
((1 * -3 + 4m * -3) + 4m * (1 + 4m)) = 0
((-3 + -12m) + 4m * (1 + 4m)) = 0
(-3 + -12m + (1 * 4m + 4m * 4m)) = 0
(-3 + -12m + (4m + 16m2)) = 0

Combine like terms: -12m + 4m = -8m
(-3 + -8m + 16m2) = 0

Solving
-3 + -8m + 16m2 = 0

Solving for variable 'm'.

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

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 '(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
Solution
m = {-0.25, 0.75}