r^2-3r-12=0

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

Simplifying
r2 + -3r + -12 = 0

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

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

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

Combine like terms: -12 + 12 = 0
0 + -3r + r2 = 0 + 12
-3r + r2 = 0 + 12

Combine like terms: 0 + 12 = 12
-3r + r2 = 12

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 = 12 + 2.25

Reorder the terms:
2.25 + -3r + r2 = 12 + 2.25

Combine like terms: 12 + 2.25 = 14.25
2.25 + -3r + r2 = 14.25

Factor a perfect square on the left side:
(r + -1.5)(r + -1.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(r + -1.5) equal to 3.774917218 and -3.774917218.

Subproblem 1
r + -1.5 = 3.774917218

Simplifying
r + -1.5 = 3.774917218

Reorder the terms:
-1.5 + r = 3.774917218

Solving
-1.5 + r = 3.774917218

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 = 3.774917218 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + r = 3.774917218 + 1.5
r = 3.774917218 + 1.5

Combine like terms: 3.774917218 + 1.5 = 5.274917218
r = 5.274917218

Simplifying
r = 5.274917218

Subproblem 2
r + -1.5 = -3.774917218

Simplifying
r + -1.5 = -3.774917218

Reorder the terms:
-1.5 + r = -3.774917218

Solving
-1.5 + r = -3.774917218

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 = -3.774917218 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + r = -3.774917218 + 1.5
r = -3.774917218 + 1.5

Combine like terms: -3.774917218 + 1.5 = -2.274917218
r = -2.274917218

Simplifying
r = -2.274917218

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {5.274917218, -2.274917218}