r^2-9r-12=0

Solution for r^2-9r-12=0 equation:

Simplifying
r2 + -9r + -12 = 0

Reorder the terms:
-12 + -9r + r2 = 0

Solving
-12 + -9r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -9r + 12 + r2 = 0 + 12

Reorder the terms:
-12 + 12 + -9r + r2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -9r + r2 = 0 + 12
-9r + r2 = 0 + 12

Combine like terms: 0 + 12 = 12
-9r + r2 = 12

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 = 12 + 20.25

Reorder the terms:
20.25 + -9r + r2 = 12 + 20.25

Combine like terms: 12 + 20.25 = 32.25
20.25 + -9r + r2 = 32.25

Factor a perfect square on the left side:
(r + -4.5)(r + -4.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(r + -4.5) equal to 5.678908346 and -5.678908346.

Subproblem 1
r + -4.5 = 5.678908346

Simplifying
r + -4.5 = 5.678908346

Reorder the terms:
-4.5 + r = 5.678908346

Solving
-4.5 + r = 5.678908346

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 = 5.678908346 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + r = 5.678908346 + 4.5
r = 5.678908346 + 4.5

Combine like terms: 5.678908346 + 4.5 = 10.178908346
r = 10.178908346

Simplifying
r = 10.178908346

Subproblem 2
r + -4.5 = -5.678908346

Simplifying
r + -4.5 = -5.678908346

Reorder the terms:
-4.5 + r = -5.678908346

Solving
-4.5 + r = -5.678908346

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 = -5.678908346 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + r = -5.678908346 + 4.5
r = -5.678908346 + 4.5

Combine like terms: -5.678908346 + 4.5 = -1.178908346
r = -1.178908346

Simplifying
r = -1.178908346

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {10.178908346, -1.178908346}