(4r+5)(r+3)=0

Solution for (4r+5)(r+3)=0 equation:

Simplifying
(4r + 5)(r + 3) = 0

Reorder the terms:
(5 + 4r)(r + 3) = 0

Reorder the terms:
(5 + 4r)(3 + r) = 0

Multiply (5 + 4r) * (3 + r)
(5(3 + r) + 4r * (3 + r)) = 0
((3 * 5 + r * 5) + 4r * (3 + r)) = 0
((15 + 5r) + 4r * (3 + r)) = 0
(15 + 5r + (3 * 4r + r * 4r)) = 0
(15 + 5r + (12r + 4r2)) = 0

Combine like terms: 5r + 12r = 17r
(15 + 17r + 4r2) = 0

Solving
15 + 17r + 4r2 = 0

Solving for variable 'r'.

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

Subproblem 1
Set the factor '(3 + r)' equal to zero and attempt to solve:

Simplifying
3 + r = 0

Solving
3 + r = 0

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

Add '-3' to each side of the equation.
3 + -3 + r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + r = 0 + -3
r = 0 + -3

Combine like terms: 0 + -3 = -3
r = -3

Simplifying
r = -3
Subproblem 2
Set the factor '(5 + 4r)' equal to zero and attempt to solve:

Simplifying
5 + 4r = 0

Solving
5 + 4r = 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 + 4r = 0 + -5

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

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

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

Simplifying
r = -1.25
Solution
r = {-3, -1.25}