(m+2)(4m+5)=0

Solution for (m+2)(4m+5)=0 equation:

Simplifying
(m + 2)(4m + 5) = 0

Reorder the terms:
(2 + m)(4m + 5) = 0

Reorder the terms:
(2 + m)(5 + 4m) = 0

Multiply (2 + m) * (5 + 4m)
(2(5 + 4m) + m(5 + 4m)) = 0
((5 * 2 + 4m * 2) + m(5 + 4m)) = 0
((10 + 8m) + m(5 + 4m)) = 0
(10 + 8m + (5 * m + 4m * m)) = 0
(10 + 8m + (5m + 4m2)) = 0

Combine like terms: 8m + 5m = 13m
(10 + 13m + 4m2) = 0

Solving
10 + 13m + 4m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(2 + m)(5 + 4m) = 0

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

Simplifying
2 + m = 0

Solving
2 + m = 0

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

Add '-2' to each side of the equation.
2 + -2 + m = 0 + -2

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

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

Simplifying
m = -2
Subproblem 2
Set the factor '(5 + 4m)' equal to zero and attempt to solve:

Simplifying
5 + 4m = 0

Solving
5 + 4m = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4m = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4m = 0 + -5
4m = 0 + -5

Combine like terms: 0 + -5 = -5
4m = -5

Divide each side by '4'.
m = -1.25

Simplifying
m = -1.25
Solution
m = {-2, -1.25}