2(4r+6)+3(r-5)=30

Solution for 2(4r+6)+3(r-5)=30 equation:

Simplifying
2(4r + 6) + 3(r + -5) = 30

Reorder the terms:
2(6 + 4r) + 3(r + -5) = 30
(6 * 2 + 4r * 2) + 3(r + -5) = 30
(12 + 8r) + 3(r + -5) = 30

Reorder the terms:
12 + 8r + 3(-5 + r) = 30
12 + 8r + (-5 * 3 + r * 3) = 30
12 + 8r + (-15 + 3r) = 30

Reorder the terms:
12 + -15 + 8r + 3r = 30

Combine like terms: 12 + -15 = -3
-3 + 8r + 3r = 30

Combine like terms: 8r + 3r = 11r
-3 + 11r = 30

Solving
-3 + 11r = 30

Solving for variable 'r'.

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

Add '3' to each side of the equation.
-3 + 3 + 11r = 30 + 3

Combine like terms: -3 + 3 = 0
0 + 11r = 30 + 3
11r = 30 + 3

Combine like terms: 30 + 3 = 33
11r = 33

Divide each side by '11'.
r = 3

Simplifying
r = 3