r(3r+6)=3

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

Simplifying
r(3r + 6) = 3

Reorder the terms:
r(6 + 3r) = 3
(6 * r + 3r * r) = 3
(6r + 3r2) = 3

Solving
6r + 3r2 = 3

Solving for variable 'r'.

Reorder the terms:
-3 + 6r + 3r2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 6r + 3r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 2r + r2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + 2r + r2)' equal to zero and attempt to solve:

Simplifying
-1 + 2r + r2 = 0

Solving
-1 + 2r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2r + 1 + r2 = 0 + 1

Reorder the terms:
-1 + 1 + 2r + r2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2r + r2 = 0 + 1
2r + r2 = 0 + 1

Combine like terms: 0 + 1 = 1
2r + r2 = 1

The r term is 2r.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2r + 1 + r2 = 1 + 1

Reorder the terms:
1 + 2r + r2 = 1 + 1

Combine like terms: 1 + 1 = 2
1 + 2r + r2 = 2

Factor a perfect square on the left side:
(r + 1)(r + 1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(r + 1) equal to 1.414213562 and -1.414213562.

Subproblem 1
r + 1 = 1.414213562

Simplifying
r + 1 = 1.414213562

Reorder the terms:
1 + r = 1.414213562

Solving
1 + r = 1.414213562

Solving for variable 'r'.

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 = 1.414213562 + -1

Combine like terms: 1 + -1 = 0
0 + r = 1.414213562 + -1
r = 1.414213562 + -1

Combine like terms: 1.414213562 + -1 = 0.414213562
r = 0.414213562

Simplifying
r = 0.414213562

Subproblem 2
r + 1 = -1.414213562

Simplifying
r + 1 = -1.414213562

Reorder the terms:
1 + r = -1.414213562

Solving
1 + r = -1.414213562

Solving for variable 'r'.

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 = -1.414213562 + -1

Combine like terms: 1 + -1 = 0
0 + r = -1.414213562 + -1
r = -1.414213562 + -1

Combine like terms: -1.414213562 + -1 = -2.414213562
r = -2.414213562

Simplifying
r = -2.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.414213562, -2.414213562}
Solution
r = {0.414213562, -2.414213562}