2(3r+1)+7(-5-2r)=23

Solution for 2(3r+1)+7(-5-2r)=23 equation:

Simplifying
2(3r + 1) + 7(-5 + -2r) = 23

Reorder the terms:
2(1 + 3r) + 7(-5 + -2r) = 23
(1 * 2 + 3r * 2) + 7(-5 + -2r) = 23
(2 + 6r) + 7(-5 + -2r) = 23
2 + 6r + (-5 * 7 + -2r * 7) = 23
2 + 6r + (-35 + -14r) = 23

Reorder the terms:
2 + -35 + 6r + -14r = 23

Combine like terms: 2 + -35 = -33
-33 + 6r + -14r = 23

Combine like terms: 6r + -14r = -8r
-33 + -8r = 23

Solving
-33 + -8r = 23

Solving for variable 'r'.

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

Add '33' to each side of the equation.
-33 + 33 + -8r = 23 + 33

Combine like terms: -33 + 33 = 0
0 + -8r = 23 + 33
-8r = 23 + 33

Combine like terms: 23 + 33 = 56
-8r = 56

Divide each side by '-8'.
r = -7

Simplifying
r = -7