(4m+1)(8m+3)=0

Solution for (4m+1)(8m+3)=0 equation:

Simplifying
(4m + 1)(8m + 3) = 0

Reorder the terms:
(1 + 4m)(8m + 3) = 0

Reorder the terms:
(1 + 4m)(3 + 8m) = 0

Multiply (1 + 4m) * (3 + 8m)
(1(3 + 8m) + 4m * (3 + 8m)) = 0
((3 * 1 + 8m * 1) + 4m * (3 + 8m)) = 0
((3 + 8m) + 4m * (3 + 8m)) = 0
(3 + 8m + (3 * 4m + 8m * 4m)) = 0
(3 + 8m + (12m + 32m2)) = 0

Combine like terms: 8m + 12m = 20m
(3 + 20m + 32m2) = 0

Solving
3 + 20m + 32m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(3 + 8m)(1 + 4m) = 0

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 + 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
Solution
m = {-0.375, -0.25}