(5r+3)(2r+6)=0

Solution for (5r+3)(2r+6)=0 equation:

Simplifying
(5r + 3)(2r + 6) = 0

Reorder the terms:
(3 + 5r)(2r + 6) = 0

Reorder the terms:
(3 + 5r)(6 + 2r) = 0

Multiply (3 + 5r) * (6 + 2r)
(3(6 + 2r) + 5r * (6 + 2r)) = 0
((6 * 3 + 2r * 3) + 5r * (6 + 2r)) = 0
((18 + 6r) + 5r * (6 + 2r)) = 0
(18 + 6r + (6 * 5r + 2r * 5r)) = 0
(18 + 6r + (30r + 10r2)) = 0

Combine like terms: 6r + 30r = 36r
(18 + 36r + 10r2) = 0

Solving
18 + 36r + 10r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 18r + 5r2) = 0

Factor a trinomial.
2((3 + r)(3 + 5r)) = 0

Ignore the factor 2.
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 '(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 = {-3, -0.6}