3(r+1)-[2(3-2r)-3(3-r)]=2(r+5)

Solution for 3(r+1)-[2(3-2r)-3(3-r)]=2(r+5) equation:

Simplifying
3(r + 1) + -1[2(3 + -2r) + -3(3 + -1r)] = 2(r + 5)

Reorder the terms:
3(1 + r) + -1[2(3 + -2r) + -3(3 + -1r)] = 2(r + 5)
(1 * 3 + r * 3) + -1[2(3 + -2r) + -3(3 + -1r)] = 2(r + 5)
(3 + 3r) + -1[2(3 + -2r) + -3(3 + -1r)] = 2(r + 5)
3 + 3r + -1[(3 * 2 + -2r * 2) + -3(3 + -1r)] = 2(r + 5)
3 + 3r + -1[(6 + -4r) + -3(3 + -1r)] = 2(r + 5)
3 + 3r + -1[6 + -4r + (3 * -3 + -1r * -3)] = 2(r + 5)
3 + 3r + -1[6 + -4r + (-9 + 3r)] = 2(r + 5)

Reorder the terms:
3 + 3r + -1[6 + -9 + -4r + 3r] = 2(r + 5)

Combine like terms: 6 + -9 = -3
3 + 3r + -1[-3 + -4r + 3r] = 2(r + 5)

Combine like terms: -4r + 3r = -1r
3 + 3r + -1[-3 + -1r] = 2(r + 5)
3 + 3r + [-3 * -1 + -1r * -1] = 2(r + 5)
3 + 3r + [3 + 1r] = 2(r + 5)

Reorder the terms:
3 + 3 + 3r + 1r = 2(r + 5)

Combine like terms: 3 + 3 = 6
6 + 3r + 1r = 2(r + 5)

Combine like terms: 3r + 1r = 4r
6 + 4r = 2(r + 5)

Reorder the terms:
6 + 4r = 2(5 + r)
6 + 4r = (5 * 2 + r * 2)
6 + 4r = (10 + 2r)

Solving
6 + 4r = 10 + 2r

Solving for variable 'r'.

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

Add '-2r' to each side of the equation.
6 + 4r + -2r = 10 + 2r + -2r

Combine like terms: 4r + -2r = 2r
6 + 2r = 10 + 2r + -2r

Combine like terms: 2r + -2r = 0
6 + 2r = 10 + 0
6 + 2r = 10

Add '-6' to each side of the equation.
6 + -6 + 2r = 10 + -6

Combine like terms: 6 + -6 = 0
0 + 2r = 10 + -6
2r = 10 + -6

Combine like terms: 10 + -6 = 4
2r = 4

Divide each side by '2'.
r = 2

Simplifying
r = 2