3(r+1)=5(r-3)+8

Solution for 3(r+1)=5(r-3)+8 equation:

Simplifying
3(r + 1) = 5(r + -3) + 8

Reorder the terms:
3(1 + r) = 5(r + -3) + 8
(1 * 3 + r * 3) = 5(r + -3) + 8
(3 + 3r) = 5(r + -3) + 8

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

Reorder the terms:
3 + 3r = -15 + 8 + 5r

Combine like terms: -15 + 8 = -7
3 + 3r = -7 + 5r

Solving
3 + 3r = -7 + 5r

Solving for variable 'r'.

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

Add '-5r' to each side of the equation.
3 + 3r + -5r = -7 + 5r + -5r

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

Combine like terms: 5r + -5r = 0
3 + -2r = -7 + 0
3 + -2r = -7

Add '-3' to each side of the equation.
3 + -3 + -2r = -7 + -3

Combine like terms: 3 + -3 = 0
0 + -2r = -7 + -3
-2r = -7 + -3

Combine like terms: -7 + -3 = -10
-2r = -10

Divide each side by '-2'.
r = 5

Simplifying
r = 5