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

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

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

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

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

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

Combine like terms: 1m + 8m = 9m
(4 + 9m + 2m2) = 0

Solving
4 + 9m + 2m2 = 0

Solving for variable 'm'.

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

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

Simplifying
4 + m = 0

Solving
4 + m = 0

Move all terms containing m to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + m = 0 + -4

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

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

Simplifying
m = -4
Subproblem 2
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
Solution
m = {-4, -0.5}