3r^2-2=6r+3

Solution for 3r^2-2=6r+3 equation:

Simplifying
3r2 + -2 = 6r + 3

Reorder the terms:
-2 + 3r2 = 6r + 3

Reorder the terms:
-2 + 3r2 = 3 + 6r

Solving
-2 + 3r2 = 3 + 6r

Solving for variable 'r'.

Reorder the terms:
-2 + -3 + -6r + 3r2 = 3 + 6r + -3 + -6r

Combine like terms: -2 + -3 = -5
-5 + -6r + 3r2 = 3 + 6r + -3 + -6r

Reorder the terms:
-5 + -6r + 3r2 = 3 + -3 + 6r + -6r

Combine like terms: 3 + -3 = 0
-5 + -6r + 3r2 = 0 + 6r + -6r
-5 + -6r + 3r2 = 6r + -6r

Combine like terms: 6r + -6r = 0
-5 + -6r + 3r2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-1.666666667 + -2r + r2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -2r + 1.666666667 + r2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -2r + r2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -2r + r2 = 0 + 1.666666667
-2r + r2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-2r + r2 = 1.666666667

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 = 1.666666667 + 1

Reorder the terms:
1 + -2r + r2 = 1.666666667 + 1

Combine like terms: 1.666666667 + 1 = 2.666666667
1 + -2r + r2 = 2.666666667

Factor a perfect square on the left side:
(r + -1)(r + -1) = 2.666666667

Calculate the square root of the right side: 1.632993162

Break this problem into two subproblems by setting 
(r + -1) equal to 1.632993162 and -1.632993162.

Subproblem 1
r + -1 = 1.632993162

Simplifying
r + -1 = 1.632993162

Reorder the terms:
-1 + r = 1.632993162

Solving
-1 + r = 1.632993162

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 = 1.632993162 + 1

Combine like terms: -1 + 1 = 0
0 + r = 1.632993162 + 1
r = 1.632993162 + 1

Combine like terms: 1.632993162 + 1 = 2.632993162
r = 2.632993162

Simplifying
r = 2.632993162

Subproblem 2
r + -1 = -1.632993162

Simplifying
r + -1 = -1.632993162

Reorder the terms:
-1 + r = -1.632993162

Solving
-1 + r = -1.632993162

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 = -1.632993162 + 1

Combine like terms: -1 + 1 = 0
0 + r = -1.632993162 + 1
r = -1.632993162 + 1

Combine like terms: -1.632993162 + 1 = -0.632993162
r = -0.632993162

Simplifying
r = -0.632993162

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.632993162, -0.632993162}