(5r+3r)(r+1)=0

Solution for (5r+3r)(r+1)=0 equation:

Simplifying
(5r + 3r)(r + 1) = 0

Combine like terms: 5r + 3r = 8r
(8r)(r + 1) = 0

Remove parenthesis around (8r)
8r(r + 1) = 0

Reorder the terms:
8r(1 + r) = 0
(1 * 8r + r * 8r) = 0
(8r + 8r2) = 0

Solving
8r + 8r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '8r'.
8r(1 + r) = 0

Ignore the factor 8.
Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
Set the factor '(1 + r)' equal to zero and attempt to solve:

Simplifying
1 + r = 0

Solving
1 + r = 0

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

Add '-1' to each side of the equation.
1 + -1 + r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + r = 0 + -1
r = 0 + -1

Combine like terms: 0 + -1 = -1
r = -1

Simplifying
r = -1
Solution
r = {0, -1}