(2r+3)(3r+1)=

Solution for (2r+3)(3r+1)= equation:

Simplifying
(2r + 3)(3r + 1) = 0

Reorder the terms:
(3 + 2r)(3r + 1) = 0

Reorder the terms:
(3 + 2r)(1 + 3r) = 0

Multiply (3 + 2r) * (1 + 3r)
(3(1 + 3r) + 2r * (1 + 3r)) = 0
((1 * 3 + 3r * 3) + 2r * (1 + 3r)) = 0
((3 + 9r) + 2r * (1 + 3r)) = 0
(3 + 9r + (1 * 2r + 3r * 2r)) = 0
(3 + 9r + (2r + 6r2)) = 0

Combine like terms: 9r + 2r = 11r
(3 + 11r + 6r2) = 0

Solving
3 + 11r + 6r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3 + 2r)(1 + 3r) = 0

Subproblem 1
Set the factor '(3 + 2r)' equal to zero and attempt to solve:

Simplifying
3 + 2r = 0

Solving
3 + 2r = 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 + 2r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2r = 0 + -3
2r = 0 + -3

Combine like terms: 0 + -3 = -3
2r = -3

Divide each side by '2'.
r = -1.5

Simplifying
r = -1.5
Subproblem 2
Set the factor '(1 + 3r)' equal to zero and attempt to solve:

Simplifying
1 + 3r = 0

Solving
1 + 3r = 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 + 3r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3r = 0 + -1
3r = 0 + -1

Combine like terms: 0 + -1 = -1
3r = -1

Divide each side by '3'.
r = -0.3333333333

Simplifying
r = -0.3333333333
Solution
r = {-1.5, -0.3333333333}