(r-4)(r+12)=11

Solution for (r-4)(r+12)=11 equation:

Simplifying
(r + -4)(r + 12) = 11

Reorder the terms:
(-4 + r)(r + 12) = 11

Reorder the terms:
(-4 + r)(12 + r) = 11

Multiply (-4 + r) * (12 + r)
(-4(12 + r) + r(12 + r)) = 11
((12 * -4 + r * -4) + r(12 + r)) = 11
((-48 + -4r) + r(12 + r)) = 11
(-48 + -4r + (12 * r + r * r)) = 11
(-48 + -4r + (12r + r2)) = 11

Combine like terms: -4r + 12r = 8r
(-48 + 8r + r2) = 11

Solving
-48 + 8r + r2 = 11

Solving for variable 'r'.

Reorder the terms:
-48 + -11 + 8r + r2 = 11 + -11

Combine like terms: -48 + -11 = -59
-59 + 8r + r2 = 11 + -11

Combine like terms: 11 + -11 = 0
-59 + 8r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '59' to each side of the equation.
-59 + 8r + 59 + r2 = 0 + 59

Reorder the terms:
-59 + 59 + 8r + r2 = 0 + 59

Combine like terms: -59 + 59 = 0
0 + 8r + r2 = 0 + 59
8r + r2 = 0 + 59

Combine like terms: 0 + 59 = 59
8r + r2 = 59

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 = 59 + 16

Reorder the terms:
16 + 8r + r2 = 59 + 16

Combine like terms: 59 + 16 = 75
16 + 8r + r2 = 75

Factor a perfect square on the left side:
(r + 4)(r + 4) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(r + 4) equal to 8.660254038 and -8.660254038.

Subproblem 1
r + 4 = 8.660254038

Simplifying
r + 4 = 8.660254038

Reorder the terms:
4 + r = 8.660254038

Solving
4 + r = 8.660254038

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 = 8.660254038 + -4

Combine like terms: 4 + -4 = 0
0 + r = 8.660254038 + -4
r = 8.660254038 + -4

Combine like terms: 8.660254038 + -4 = 4.660254038
r = 4.660254038

Simplifying
r = 4.660254038

Subproblem 2
r + 4 = -8.660254038

Simplifying
r + 4 = -8.660254038

Reorder the terms:
4 + r = -8.660254038

Solving
4 + r = -8.660254038

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 = -8.660254038 + -4

Combine like terms: 4 + -4 = 0
0 + r = -8.660254038 + -4
r = -8.660254038 + -4

Combine like terms: -8.660254038 + -4 = -12.660254038
r = -12.660254038

Simplifying
r = -12.660254038

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.660254038, -12.660254038}