(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 = 7m
(-4 + 7m + 2m2) = 0

Solving
-4 + 7m + 2m2 = 0

Solving for variable 'm'.

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

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

Simplifying
-4 + -1m = 0

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

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

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

Divide each side by '-1'.
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}