(2r-3)+7(2-r)=3(r+2)-7

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

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

Reorder the terms:
(-3 + 2r) + 7(2 + -1r) = 3(r + 2) + -7

Remove parenthesis around (-3 + 2r)
-3 + 2r + 7(2 + -1r) = 3(r + 2) + -7
-3 + 2r + (2 * 7 + -1r * 7) = 3(r + 2) + -7
-3 + 2r + (14 + -7r) = 3(r + 2) + -7

Reorder the terms:
-3 + 14 + 2r + -7r = 3(r + 2) + -7

Combine like terms: -3 + 14 = 11
11 + 2r + -7r = 3(r + 2) + -7

Combine like terms: 2r + -7r = -5r
11 + -5r = 3(r + 2) + -7

Reorder the terms:
11 + -5r = 3(2 + r) + -7
11 + -5r = (2 * 3 + r * 3) + -7
11 + -5r = (6 + 3r) + -7

Reorder the terms:
11 + -5r = 6 + -7 + 3r

Combine like terms: 6 + -7 = -1
11 + -5r = -1 + 3r

Solving
11 + -5r = -1 + 3r

Solving for variable 'r'.

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

Add '-3r' to each side of the equation.
11 + -5r + -3r = -1 + 3r + -3r

Combine like terms: -5r + -3r = -8r
11 + -8r = -1 + 3r + -3r

Combine like terms: 3r + -3r = 0
11 + -8r = -1 + 0
11 + -8r = -1

Add '-11' to each side of the equation.
11 + -11 + -8r = -1 + -11

Combine like terms: 11 + -11 = 0
0 + -8r = -1 + -11
-8r = -1 + -11

Combine like terms: -1 + -11 = -12
-8r = -12

Divide each side by '-8'.
r = 1.5

Simplifying
r = 1.5