3[2(2r+3)-(r+1)-(r+2)]=0

Solution for 3[2(2r+3)-(r+1)-(r+2)]=0 equation:

Simplifying
3[2(2r + 3) + -1(r + 1) + -1(r + 2)] = 0

Reorder the terms:
3[2(3 + 2r) + -1(r + 1) + -1(r + 2)] = 0
3[(3 * 2 + 2r * 2) + -1(r + 1) + -1(r + 2)] = 0
3[(6 + 4r) + -1(r + 1) + -1(r + 2)] = 0

Reorder the terms:
3[6 + 4r + -1(1 + r) + -1(r + 2)] = 0
3[6 + 4r + (1 * -1 + r * -1) + -1(r + 2)] = 0
3[6 + 4r + (-1 + -1r) + -1(r + 2)] = 0

Reorder the terms:
3[6 + 4r + -1 + -1r + -1(2 + r)] = 0
3[6 + 4r + -1 + -1r + (2 * -1 + r * -1)] = 0
3[6 + 4r + -1 + -1r + (-2 + -1r)] = 0

Reorder the terms:
3[6 + -1 + -2 + 4r + -1r + -1r] = 0

Combine like terms: 6 + -1 = 5
3[5 + -2 + 4r + -1r + -1r] = 0

Combine like terms: 5 + -2 = 3
3[3 + 4r + -1r + -1r] = 0

Combine like terms: 4r + -1r = 3r
3[3 + 3r + -1r] = 0

Combine like terms: 3r + -1r = 2r
3[3 + 2r] = 0
[3 * 3 + 2r * 3] = 0
[9 + 6r] = 0

Solving
9 + 6r = 0

Solving for variable 'r'.

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

Add '-9' to each side of the equation.
9 + -9 + 6r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 6r = 0 + -9
6r = 0 + -9

Combine like terms: 0 + -9 = -9
6r = -9

Divide each side by '6'.
r = -1.5

Simplifying
r = -1.5