2(r-11)=(r-5)(r+3)-13

Solution for 2(r-11)=(r-5)(r+3)-13 equation:

Simplifying
2(r + -11) = (r + -5)(r + 3) + -13

Reorder the terms:
2(-11 + r) = (r + -5)(r + 3) + -13
(-11 * 2 + r * 2) = (r + -5)(r + 3) + -13
(-22 + 2r) = (r + -5)(r + 3) + -13

Reorder the terms:
-22 + 2r = (-5 + r)(r + 3) + -13

Reorder the terms:
-22 + 2r = (-5 + r)(3 + r) + -13

Multiply (-5 + r) * (3 + r)
-22 + 2r = (-5(3 + r) + r(3 + r)) + -13
-22 + 2r = ((3 * -5 + r * -5) + r(3 + r)) + -13
-22 + 2r = ((-15 + -5r) + r(3 + r)) + -13
-22 + 2r = (-15 + -5r + (3 * r + r * r)) + -13
-22 + 2r = (-15 + -5r + (3r + r2)) + -13

Combine like terms: -5r + 3r = -2r
-22 + 2r = (-15 + -2r + r2) + -13

Reorder the terms:
-22 + 2r = -15 + -13 + -2r + r2

Combine like terms: -15 + -13 = -28
-22 + 2r = -28 + -2r + r2

Solving
-22 + 2r = -28 + -2r + r2

Solving for variable 'r'.

Reorder the terms:
-22 + 28 + 2r + 2r + -1r2 = -28 + -2r + r2 + 28 + 2r + -1r2

Combine like terms: -22 + 28 = 6
6 + 2r + 2r + -1r2 = -28 + -2r + r2 + 28 + 2r + -1r2

Combine like terms: 2r + 2r = 4r
6 + 4r + -1r2 = -28 + -2r + r2 + 28 + 2r + -1r2

Reorder the terms:
6 + 4r + -1r2 = -28 + 28 + -2r + 2r + r2 + -1r2

Combine like terms: -28 + 28 = 0
6 + 4r + -1r2 = 0 + -2r + 2r + r2 + -1r2
6 + 4r + -1r2 = -2r + 2r + r2 + -1r2

Combine like terms: -2r + 2r = 0
6 + 4r + -1r2 = 0 + r2 + -1r2
6 + 4r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
6 + 4r + -1r2 = 0

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

Divide each side by '-1'.
-6 + -4r + r2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -4r + 6 + r2 = 0 + 6

Reorder the terms:
-6 + 6 + -4r + r2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -4r + r2 = 0 + 6
-4r + r2 = 0 + 6

Combine like terms: 0 + 6 = 6
-4r + r2 = 6

The r term is -4r.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4r + 4 + r2 = 6 + 4

Reorder the terms:
4 + -4r + r2 = 6 + 4

Combine like terms: 6 + 4 = 10
4 + -4r + r2 = 10

Factor a perfect square on the left side:
(r + -2)(r + -2) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(r + -2) equal to 3.16227766 and -3.16227766.

Subproblem 1
r + -2 = 3.16227766

Simplifying
r + -2 = 3.16227766

Reorder the terms:
-2 + r = 3.16227766

Solving
-2 + r = 3.16227766

Solving for variable 'r'.

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

Add '2' to each side of the equation.
-2 + 2 + r = 3.16227766 + 2

Combine like terms: -2 + 2 = 0
0 + r = 3.16227766 + 2
r = 3.16227766 + 2

Combine like terms: 3.16227766 + 2 = 5.16227766
r = 5.16227766

Simplifying
r = 5.16227766

Subproblem 2
r + -2 = -3.16227766

Simplifying
r + -2 = -3.16227766

Reorder the terms:
-2 + r = -3.16227766

Solving
-2 + r = -3.16227766

Solving for variable 'r'.

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

Add '2' to each side of the equation.
-2 + 2 + r = -3.16227766 + 2

Combine like terms: -2 + 2 = 0
0 + r = -3.16227766 + 2
r = -3.16227766 + 2

Combine like terms: -3.16227766 + 2 = -1.16227766
r = -1.16227766

Simplifying
r = -1.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {5.16227766, -1.16227766}