3r(r+1)=

Solution for 3r(r+1)= equation:

Simplifying
3r(r + 1) = 0

Reorder the terms:
3r(1 + r) = 0
(1 * 3r + r * 3r) = 0
(3r + 3r2) = 0

Solving
3r + 3r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3r'.
3r(1 + r) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
Set the factor '(1 + r)' equal to zero and attempt to solve:

Simplifying
1 + r = 0

Solving
1 + r = 0

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

Add '-1' to each side of the equation.
1 + -1 + r = 0 + -1

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

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

Simplifying
r = -1
Solution
r = {0, -1}