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

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

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

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

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

Multiply (3 + 4r) * (3 + 5r)
(3(3 + 5r) + 4r * (3 + 5r)) = 0
((3 * 3 + 5r * 3) + 4r * (3 + 5r)) = 0
((9 + 15r) + 4r * (3 + 5r)) = 0
(9 + 15r + (3 * 4r + 5r * 4r)) = 0
(9 + 15r + (12r + 20r2)) = 0

Combine like terms: 15r + 12r = 27r
(9 + 27r + 20r2) = 0

Solving
9 + 27r + 20r2 = 0

Solving for variable 'r'.

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

Subproblem 1
Set the factor '(3 + 4r)' equal to zero and attempt to solve:

Simplifying
3 + 4r = 0

Solving
3 + 4r = 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 + 4r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4r = 0 + -3
4r = 0 + -3

Combine like terms: 0 + -3 = -3
4r = -3

Divide each side by '4'.
r = -0.75

Simplifying
r = -0.75
Subproblem 2
Set the factor '(3 + 5r)' equal to zero and attempt to solve:

Simplifying
3 + 5r = 0

Solving
3 + 5r = 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 + 5r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5r = 0 + -3
5r = 0 + -3

Combine like terms: 0 + -3 = -3
5r = -3

Divide each side by '5'.
r = -0.6

Simplifying
r = -0.6
Solution
r = {-0.75, -0.6}