r^2+8r-12=0

Solution for r^2+8r-12=0 equation:

Simplifying
r2 + 8r + -12 = 0

Reorder the terms:
-12 + 8r + r2 = 0

Solving
-12 + 8r + 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 + 8r + 12 + r2 = 0 + 12

Reorder the terms:
-12 + 12 + 8r + r2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 8r + r2 = 0 + 12
8r + r2 = 0 + 12

Combine like terms: 0 + 12 = 12
8r + r2 = 12

The r term is 8r.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8r + 16 + r2 = 12 + 16

Reorder the terms:
16 + 8r + r2 = 12 + 16

Combine like terms: 12 + 16 = 28
16 + 8r + r2 = 28

Factor a perfect square on the left side:
(r + 4)(r + 4) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(r + 4) equal to 5.291502622 and -5.291502622.

Subproblem 1
r + 4 = 5.291502622

Simplifying
r + 4 = 5.291502622

Reorder the terms:
4 + r = 5.291502622

Solving
4 + r = 5.291502622

Solving for variable 'r'.

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

Add '-4' to each side of the equation.
4 + -4 + r = 5.291502622 + -4

Combine like terms: 4 + -4 = 0
0 + r = 5.291502622 + -4
r = 5.291502622 + -4

Combine like terms: 5.291502622 + -4 = 1.291502622
r = 1.291502622

Simplifying
r = 1.291502622

Subproblem 2
r + 4 = -5.291502622

Simplifying
r + 4 = -5.291502622

Reorder the terms:
4 + r = -5.291502622

Solving
4 + r = -5.291502622

Solving for variable 'r'.

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

Add '-4' to each side of the equation.
4 + -4 + r = -5.291502622 + -4

Combine like terms: 4 + -4 = 0
0 + r = -5.291502622 + -4
r = -5.291502622 + -4

Combine like terms: -5.291502622 + -4 = -9.291502622
r = -9.291502622

Simplifying
r = -9.291502622

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.291502622, -9.291502622}