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

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

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

Reorder the terms:
(5 + 3r)(r + 1) = 0

Reorder the terms:
(5 + 3r)(1 + r) = 0

Multiply (5 + 3r) * (1 + r)
(5(1 + r) + 3r * (1 + r)) = 0
((1 * 5 + r * 5) + 3r * (1 + r)) = 0
((5 + 5r) + 3r * (1 + r)) = 0
(5 + 5r + (1 * 3r + r * 3r)) = 0
(5 + 5r + (3r + 3r2)) = 0

Combine like terms: 5r + 3r = 8r
(5 + 8r + 3r2) = 0

Solving
5 + 8r + 3r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(5 + 3r)(1 + r) = 0

Subproblem 1
Set the factor '(5 + 3r)' equal to zero and attempt to solve:

Simplifying
5 + 3r = 0

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

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

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

Divide each side by '3'.
r = -1.666666667

Simplifying
r = -1.666666667
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 = {-1.666666667, -1}