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

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

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

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

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

Multiply (1 + 4m) * (1 + 2m)
(1(1 + 2m) + 4m * (1 + 2m)) = 0
((1 * 1 + 2m * 1) + 4m * (1 + 2m)) = 0
((1 + 2m) + 4m * (1 + 2m)) = 0
(1 + 2m + (1 * 4m + 2m * 4m)) = 0
(1 + 2m + (4m + 8m2)) = 0

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

Solving
1 + 6m + 8m2 = 0

Solving for variable 'm'.

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

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

Simplifying
1 + 2m = 0

Solving
1 + 2m = 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 + 2m = 0 + -1

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

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

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

Simplifying
m = -0.5
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 = {-0.5, -0.25}