3r^2-27r=3

Solution for 3r^2-27r=3 equation:

Simplifying
3r2 + -27r = 3

Reorder the terms:
-27r + 3r2 = 3

Solving
-27r + 3r2 = 3

Solving for variable 'r'.

Reorder the terms:
-3 + -27r + 3r2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -27r + 3r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -9r + r2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -9r + r2)' equal to zero and attempt to solve:

Simplifying
-1 + -9r + r2 = 0

Solving
-1 + -9r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -9r + 1 + r2 = 0 + 1

Reorder the terms:
-1 + 1 + -9r + r2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -9r + r2 = 0 + 1
-9r + r2 = 0 + 1

Combine like terms: 0 + 1 = 1
-9r + r2 = 1

The r term is -9r.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9r + 20.25 + r2 = 1 + 20.25

Reorder the terms:
20.25 + -9r + r2 = 1 + 20.25

Combine like terms: 1 + 20.25 = 21.25
20.25 + -9r + r2 = 21.25

Factor a perfect square on the left side:
(r + -4.5)(r + -4.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(r + -4.5) equal to 4.609772229 and -4.609772229.

Subproblem 1
r + -4.5 = 4.609772229

Simplifying
r + -4.5 = 4.609772229

Reorder the terms:
-4.5 + r = 4.609772229

Solving
-4.5 + r = 4.609772229

Solving for variable 'r'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + r = 4.609772229 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + r = 4.609772229 + 4.5
r = 4.609772229 + 4.5

Combine like terms: 4.609772229 + 4.5 = 9.109772229
r = 9.109772229

Simplifying
r = 9.109772229

Subproblem 2
r + -4.5 = -4.609772229

Simplifying
r + -4.5 = -4.609772229

Reorder the terms:
-4.5 + r = -4.609772229

Solving
-4.5 + r = -4.609772229

Solving for variable 'r'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + r = -4.609772229 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + r = -4.609772229 + 4.5
r = -4.609772229 + 4.5

Combine like terms: -4.609772229 + 4.5 = -0.109772229
r = -0.109772229

Simplifying
r = -0.109772229

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {9.109772229, -0.109772229}
Solution
r = {9.109772229, -0.109772229}