3r^2-12r-228=0

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Solution for 3r^2-12r-228=0 equation: 


Simplifying
3r2 + -12r + -228 = 0

Reorder the terms:
-228 + -12r + 3r2 = 0

Solving
-228 + -12r + 3r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-76 + -4r + r2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-76 + -4r + r2)' equal to zero and attempt to solve:

Simplifying
-76 + -4r + r2 = 0

Solving
-76 + -4r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '76' to each side of the equation.
-76 + -4r + 76 + r2 = 0 + 76

Reorder the terms:
-76 + 76 + -4r + r2 = 0 + 76

Combine like terms: -76 + 76 = 0
0 + -4r + r2 = 0 + 76
-4r + r2 = 0 + 76

Combine like terms: 0 + 76 = 76
-4r + r2 = 76

The r term is -4r.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4r + 4 + r2 = 76 + 4

Reorder the terms:
4 + -4r + r2 = 76 + 4

Combine like terms: 76 + 4 = 80
4 + -4r + r2 = 80

Factor a perfect square on the left side:
(r + -2)(r + -2) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(r + -2) equal to 8.94427191 and -8.94427191.


Subproblem 1
r + -2 = 8.94427191

Simplifying
r + -2 = 8.94427191

Reorder the terms:
-2 + r = 8.94427191

Solving
-2 + r = 8.94427191

Solving for variable 'r'.

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

Add '2' to each side of the equation.
-2 + 2 + r = 8.94427191 + 2

Combine like terms: -2 + 2 = 0
0 + r = 8.94427191 + 2
r = 8.94427191 + 2

Combine like terms: 8.94427191 + 2 = 10.94427191
r = 10.94427191

Simplifying
r = 10.94427191


Subproblem 2
r + -2 = -8.94427191

Simplifying
r + -2 = -8.94427191

Reorder the terms:
-2 + r = -8.94427191

Solving
-2 + r = -8.94427191

Solving for variable 'r'.

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

Add '2' to each side of the equation.
-2 + 2 + r = -8.94427191 + 2

Combine like terms: -2 + 2 = 0
0 + r = -8.94427191 + 2
r = -8.94427191 + 2

Combine like terms: -8.94427191 + 2 = -6.94427191
r = -6.94427191

Simplifying
r = -6.94427191


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {10.94427191, -6.94427191}
Solution
r = {10.94427191, -6.94427191}

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