r(6r+1)=0

Solution for r(6r+1)=0 equation:

Simplifying
r(6r + 1) = 0

Reorder the terms:
r(1 + 6r) = 0
(1 * r + 6r * r) = 0
(1r + 6r2) = 0

Solving
1r + 6r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(1 + 6r) = 0

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 + 6r)' equal to zero and attempt to solve:

Simplifying
1 + 6r = 0

Solving
1 + 6r = 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 + 6r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6r = 0 + -1
6r = 0 + -1

Combine like terms: 0 + -1 = -1
6r = -1

Divide each side by '6'.
r = -0.1666666667

Simplifying
r = -0.1666666667
Solution
r = {0, -0.1666666667}