2(4r+6)+3(5+3r)=78

Solution for 2(4r+6)+3(5+3r)=78 equation:

Simplifying
2(4r + 6) + 3(5 + 3r) = 78

Reorder the terms:
2(6 + 4r) + 3(5 + 3r) = 78
(6 * 2 + 4r * 2) + 3(5 + 3r) = 78
(12 + 8r) + 3(5 + 3r) = 78
12 + 8r + (5 * 3 + 3r * 3) = 78
12 + 8r + (15 + 9r) = 78

Reorder the terms:
12 + 15 + 8r + 9r = 78

Combine like terms: 12 + 15 = 27
27 + 8r + 9r = 78

Combine like terms: 8r + 9r = 17r
27 + 17r = 78

Solving
27 + 17r = 78

Solving for variable 'r'.

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

Add '-27' to each side of the equation.
27 + -27 + 17r = 78 + -27

Combine like terms: 27 + -27 = 0
0 + 17r = 78 + -27
17r = 78 + -27

Combine like terms: 78 + -27 = 51
17r = 51

Divide each side by '17'.
r = 3

Simplifying
r = 3