(3r+1)2+(r+2)2=65

Solution for (3r+1)2+(r+2)2=65 equation:

Simplifying
(3r + 1) * 2 + (r + 2) * 2 = 65

Reorder the terms:
(1 + 3r) * 2 + (r + 2) * 2 = 65

Reorder the terms for easier multiplication:
2(1 + 3r) + (r + 2) * 2 = 65
(1 * 2 + 3r * 2) + (r + 2) * 2 = 65
(2 + 6r) + (r + 2) * 2 = 65

Reorder the terms:
2 + 6r + (2 + r) * 2 = 65

Reorder the terms for easier multiplication:
2 + 6r + 2(2 + r) = 65
2 + 6r + (2 * 2 + r * 2) = 65
2 + 6r + (4 + 2r) = 65

Reorder the terms:
2 + 4 + 6r + 2r = 65

Combine like terms: 2 + 4 = 6
6 + 6r + 2r = 65

Combine like terms: 6r + 2r = 8r
6 + 8r = 65

Solving
6 + 8r = 65

Solving for variable 'r'.

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

Add '-6' to each side of the equation.
6 + -6 + 8r = 65 + -6

Combine like terms: 6 + -6 = 0
0 + 8r = 65 + -6
8r = 65 + -6

Combine like terms: 65 + -6 = 59
8r = 59

Divide each side by '8'.
r = 7.375

Simplifying
r = 7.375