-3r^2+87r+111=0

Solution for -3r^2+87r+111=0 equation:

Simplifying
-3r2 + 87r + 111 = 0

Reorder the terms:
111 + 87r + -3r2 = 0

Solving
111 + 87r + -3r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(37 + 29r + -1r2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(37 + 29r + -1r2)' equal to zero and attempt to solve:

Simplifying
37 + 29r + -1r2 = 0

Solving
37 + 29r + -1r2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-37 + -29r + r2 = 0

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + -29r + 37 + r2 = 0 + 37

Reorder the terms:
-37 + 37 + -29r + r2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + -29r + r2 = 0 + 37
-29r + r2 = 0 + 37

Combine like terms: 0 + 37 = 37
-29r + r2 = 37

The r term is -29r.  Take half its coefficient (-14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
-29r + 210.25 + r2 = 37 + 210.25

Reorder the terms:
210.25 + -29r + r2 = 37 + 210.25

Combine like terms: 37 + 210.25 = 247.25
210.25 + -29r + r2 = 247.25

Factor a perfect square on the left side:
(r + -14.5)(r + -14.5) = 247.25

Calculate the square root of the right side: 15.724185194

Break this problem into two subproblems by setting 
(r + -14.5) equal to 15.724185194 and -15.724185194.

Subproblem 1
r + -14.5 = 15.724185194

Simplifying
r + -14.5 = 15.724185194

Reorder the terms:
-14.5 + r = 15.724185194

Solving
-14.5 + r = 15.724185194

Solving for variable 'r'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + r = 15.724185194 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + r = 15.724185194 + 14.5
r = 15.724185194 + 14.5

Combine like terms: 15.724185194 + 14.5 = 30.224185194
r = 30.224185194

Simplifying
r = 30.224185194

Subproblem 2
r + -14.5 = -15.724185194

Simplifying
r + -14.5 = -15.724185194

Reorder the terms:
-14.5 + r = -15.724185194

Solving
-14.5 + r = -15.724185194

Solving for variable 'r'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + r = -15.724185194 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + r = -15.724185194 + 14.5
r = -15.724185194 + 14.5

Combine like terms: -15.724185194 + 14.5 = -1.224185194
r = -1.224185194

Simplifying
r = -1.224185194

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {30.224185194, -1.224185194}
Solution
r = {30.224185194, -1.224185194}