3r(3r+1)=2

Solution for 3r(3r+1)=2 equation:

Simplifying
3r(3r + 1) = 2

Reorder the terms:
3r(1 + 3r) = 2
(1 * 3r + 3r * 3r) = 2
(3r + 9r2) = 2

Solving
3r + 9r2 = 2

Solving for variable 'r'.

Reorder the terms:
-2 + 3r + 9r2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 3r + 9r2 = 0

Factor a trinomial.
(-2 + -3r)(1 + -3r) = 0

Subproblem 1
Set the factor '(-2 + -3r)' equal to zero and attempt to solve:

Simplifying
-2 + -3r = 0

Solving
-2 + -3r = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3r = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3r = 0 + 2
-3r = 0 + 2

Combine like terms: 0 + 2 = 2
-3r = 2

Divide each side by '-3'.
r = -0.6666666667

Simplifying
r = -0.6666666667
Subproblem 2
Set the factor '(1 + -3r)' equal to zero and attempt to solve:

Simplifying
1 + -3r = 0

Solving
1 + -3r = 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 + -3r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3r = 0 + -1
-3r = 0 + -1

Combine like terms: 0 + -1 = -1
-3r = -1

Divide each side by '-3'.
r = 0.3333333333

Simplifying
r = 0.3333333333
Solution
r = {-0.6666666667, 0.3333333333}