0=2r^2+6r-72

Solution for 0=2r^2+6r-72 equation:

Simplifying
0 = 2r2 + 6r + -72

Reorder the terms:
0 = -72 + 6r + 2r2

Solving
0 = -72 + 6r + 2r2

Solving for variable 'r'.

Combine like terms: 0 + 72 = 72
72 + -6r + -2r2 = -72 + 6r + 2r2 + 72 + -6r + -2r2

Reorder the terms:
72 + -6r + -2r2 = -72 + 72 + 6r + -6r + 2r2 + -2r2

Combine like terms: -72 + 72 = 0
72 + -6r + -2r2 = 0 + 6r + -6r + 2r2 + -2r2
72 + -6r + -2r2 = 6r + -6r + 2r2 + -2r2

Combine like terms: 6r + -6r = 0
72 + -6r + -2r2 = 0 + 2r2 + -2r2
72 + -6r + -2r2 = 2r2 + -2r2

Combine like terms: 2r2 + -2r2 = 0
72 + -6r + -2r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(36 + -3r + -1r2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(36 + -3r + -1r2)' equal to zero and attempt to solve:

Simplifying
36 + -3r + -1r2 = 0

Solving
36 + -3r + -1r2 = 0

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

Divide each side by '-1'.
-36 + 3r + r2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 3r + 36 + r2 = 0 + 36

Reorder the terms:
-36 + 36 + 3r + r2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 3r + r2 = 0 + 36
3r + r2 = 0 + 36

Combine like terms: 0 + 36 = 36
3r + r2 = 36

The r term is 3r.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3r + 2.25 + r2 = 36 + 2.25

Reorder the terms:
2.25 + 3r + r2 = 36 + 2.25

Combine like terms: 36 + 2.25 = 38.25
2.25 + 3r + r2 = 38.25

Factor a perfect square on the left side:
(r + 1.5)(r + 1.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(r + 1.5) equal to 6.184658438 and -6.184658438.

Subproblem 1
r + 1.5 = 6.184658438

Simplifying
r + 1.5 = 6.184658438

Reorder the terms:
1.5 + r = 6.184658438

Solving
1.5 + r = 6.184658438

Solving for variable 'r'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + r = 6.184658438 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + r = 6.184658438 + -1.5
r = 6.184658438 + -1.5

Combine like terms: 6.184658438 + -1.5 = 4.684658438
r = 4.684658438

Simplifying
r = 4.684658438

Subproblem 2
r + 1.5 = -6.184658438

Simplifying
r + 1.5 = -6.184658438

Reorder the terms:
1.5 + r = -6.184658438

Solving
1.5 + r = -6.184658438

Solving for variable 'r'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + r = -6.184658438 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + r = -6.184658438 + -1.5
r = -6.184658438 + -1.5

Combine like terms: -6.184658438 + -1.5 = -7.684658438
r = -7.684658438

Simplifying
r = -7.684658438

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.684658438, -7.684658438}
Solution
r = {4.684658438, -7.684658438}