3(1+3r)=7(-5+r)+8

Solution for 3(1+3r)=7(-5+r)+8 equation:

Simplifying
3(1 + 3r) = 7(-5 + r) + 8
(1 * 3 + 3r * 3) = 7(-5 + r) + 8
(3 + 9r) = 7(-5 + r) + 8
3 + 9r = (-5 * 7 + r * 7) + 8
3 + 9r = (-35 + 7r) + 8

Reorder the terms:
3 + 9r = -35 + 8 + 7r

Combine like terms: -35 + 8 = -27
3 + 9r = -27 + 7r

Solving
3 + 9r = -27 + 7r

Solving for variable 'r'.

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

Add '-7r' to each side of the equation.
3 + 9r + -7r = -27 + 7r + -7r

Combine like terms: 9r + -7r = 2r
3 + 2r = -27 + 7r + -7r

Combine like terms: 7r + -7r = 0
3 + 2r = -27 + 0
3 + 2r = -27

Add '-3' to each side of the equation.
3 + -3 + 2r = -27 + -3

Combine like terms: 3 + -3 = 0
0 + 2r = -27 + -3
2r = -27 + -3

Combine like terms: -27 + -3 = -30
2r = -30

Divide each side by '2'.
r = -15

Simplifying
r = -15