(3r+1)(r+1)=65

Solution for (3r+1)(r+1)=65 equation:

Simplifying
(3r + 1)(r + 1) = 65

Reorder the terms:
(1 + 3r)(r + 1) = 65

Reorder the terms:
(1 + 3r)(1 + r) = 65

Multiply (1 + 3r) * (1 + r)
(1(1 + r) + 3r * (1 + r)) = 65
((1 * 1 + r * 1) + 3r * (1 + r)) = 65
((1 + 1r) + 3r * (1 + r)) = 65
(1 + 1r + (1 * 3r + r * 3r)) = 65
(1 + 1r + (3r + 3r2)) = 65

Combine like terms: 1r + 3r = 4r
(1 + 4r + 3r2) = 65

Solving
1 + 4r + 3r2 = 65

Solving for variable 'r'.

Reorder the terms:
1 + -65 + 4r + 3r2 = 65 + -65

Combine like terms: 1 + -65 = -64
-64 + 4r + 3r2 = 65 + -65

Combine like terms: 65 + -65 = 0
-64 + 4r + 3r2 = 0

Factor a trinomial.
(-16 + -3r)(4 + -1r) = 0

Subproblem 1
Set the factor '(-16 + -3r)' equal to zero and attempt to solve:

Simplifying
-16 + -3r = 0

Solving
-16 + -3r = 0

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

Add '16' to each side of the equation.
-16 + 16 + -3r = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -3r = 0 + 16
-3r = 0 + 16

Combine like terms: 0 + 16 = 16
-3r = 16

Divide each side by '-3'.
r = -5.333333333

Simplifying
r = -5.333333333
Subproblem 2
Set the factor '(4 + -1r)' equal to zero and attempt to solve:

Simplifying
4 + -1r = 0

Solving
4 + -1r = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1r = 0 + -4
-1r = 0 + -4

Combine like terms: 0 + -4 = -4
-1r = -4

Divide each side by '-1'.
r = 4

Simplifying
r = 4
Solution
r = {-5.333333333, 4}