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

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

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

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

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

Multiply (5 + 2r) * (4 + r)
(5(4 + r) + 2r * (4 + r)) = 0
((4 * 5 + r * 5) + 2r * (4 + r)) = 0
((20 + 5r) + 2r * (4 + r)) = 0
(20 + 5r + (4 * 2r + r * 2r)) = 0
(20 + 5r + (8r + 2r2)) = 0

Combine like terms: 5r + 8r = 13r
(20 + 13r + 2r2) = 0

Solving
20 + 13r + 2r2 = 0

Solving for variable 'r'.

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

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

Simplifying
4 + r = 0

Solving
4 + r = 0

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

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

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

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

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

Simplifying
5 + 2r = 0

Solving
5 + 2r = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2r = 0 + -5
2r = 0 + -5

Combine like terms: 0 + -5 = -5
2r = -5

Divide each side by '2'.
r = -2.5

Simplifying
r = -2.5
Solution
r = {-4, -2.5}