6r(3r+t)=

Solution for 6r(3r+t)= equation:

Simplifying
6r(3r + t) = 0
(3r * 6r + t * 6r) = 0

Reorder the terms:
(6rt + 18r2) = 0
(6rt + 18r2) = 0

Solving
6rt + 18r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '6r'.
6r(t + 3r) = 0

Ignore the factor 6.
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 '(t + 3r)' equal to zero and attempt to solve:

Simplifying
t + 3r = 0

Reorder the terms:
3r + t = 0

Solving
3r + t = 0

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

Add '-1t' to each side of the equation.
3r + t + -1t = 0 + -1t

Combine like terms: t + -1t = 0
3r + 0 = 0 + -1t
3r = 0 + -1t
Remove the zero:
3r = -1t

Divide each side by '3'.
r = -0.3333333333t

Simplifying
r = -0.3333333333t
Solution
r = {0, -0.3333333333t}