64(r+6)+64(r-6)=20(r^2-64)

Solution for 64(r+6)+64(r-6)=20(r^2-64) equation:

Simplifying
64(r + 6) + 64(r + -6) = 20(r2 + -64)

Reorder the terms:
64(6 + r) + 64(r + -6) = 20(r2 + -64)
(6 * 64 + r * 64) + 64(r + -6) = 20(r2 + -64)
(384 + 64r) + 64(r + -6) = 20(r2 + -64)

Reorder the terms:
384 + 64r + 64(-6 + r) = 20(r2 + -64)
384 + 64r + (-6 * 64 + r * 64) = 20(r2 + -64)
384 + 64r + (-384 + 64r) = 20(r2 + -64)

Reorder the terms:
384 + -384 + 64r + 64r = 20(r2 + -64)

Combine like terms: 384 + -384 = 0
0 + 64r + 64r = 20(r2 + -64)
64r + 64r = 20(r2 + -64)

Combine like terms: 64r + 64r = 128r
128r = 20(r2 + -64)

Reorder the terms:
128r = 20(-64 + r2)
128r = (-64 * 20 + r2 * 20)
128r = (-1280 + 20r2)

Solving
128r = -1280 + 20r2

Solving for variable 'r'.

Reorder the terms:
1280 + 128r + -20r2 = -1280 + 20r2 + 1280 + -20r2

Reorder the terms:
1280 + 128r + -20r2 = -1280 + 1280 + 20r2 + -20r2

Combine like terms: -1280 + 1280 = 0
1280 + 128r + -20r2 = 0 + 20r2 + -20r2
1280 + 128r + -20r2 = 20r2 + -20r2

Combine like terms: 20r2 + -20r2 = 0
1280 + 128r + -20r2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(320 + 32r + -5r2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(320 + 32r + -5r2)' equal to zero and attempt to solve:

Simplifying
320 + 32r + -5r2 = 0

Solving
320 + 32r + -5r2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-64 + -6.4r + r2 = 0

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + -6.4r + 64 + r2 = 0 + 64

Reorder the terms:
-64 + 64 + -6.4r + r2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + -6.4r + r2 = 0 + 64
-6.4r + r2 = 0 + 64

Combine like terms: 0 + 64 = 64
-6.4r + r2 = 64

The r term is -6.4r.  Take half its coefficient (-3.2).
Square it (10.24) and add it to both sides.

Add '10.24' to each side of the equation.
-6.4r + 10.24 + r2 = 64 + 10.24

Reorder the terms:
10.24 + -6.4r + r2 = 64 + 10.24

Combine like terms: 64 + 10.24 = 74.24
10.24 + -6.4r + r2 = 74.24

Factor a perfect square on the left side:
(r + -3.2)(r + -3.2) = 74.24

Calculate the square root of the right side: 8.616263691

Break this problem into two subproblems by setting 
(r + -3.2) equal to 8.616263691 and -8.616263691.

Subproblem 1
r + -3.2 = 8.616263691

Simplifying
r + -3.2 = 8.616263691

Reorder the terms:
-3.2 + r = 8.616263691

Solving
-3.2 + r = 8.616263691

Solving for variable 'r'.

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

Add '3.2' to each side of the equation.
-3.2 + 3.2 + r = 8.616263691 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + r = 8.616263691 + 3.2
r = 8.616263691 + 3.2

Combine like terms: 8.616263691 + 3.2 = 11.816263691
r = 11.816263691

Simplifying
r = 11.816263691

Subproblem 2
r + -3.2 = -8.616263691

Simplifying
r + -3.2 = -8.616263691

Reorder the terms:
-3.2 + r = -8.616263691

Solving
-3.2 + r = -8.616263691

Solving for variable 'r'.

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

Add '3.2' to each side of the equation.
-3.2 + 3.2 + r = -8.616263691 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + r = -8.616263691 + 3.2
r = -8.616263691 + 3.2

Combine like terms: -8.616263691 + 3.2 = -5.416263691
r = -5.416263691

Simplifying
r = -5.416263691

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {11.816263691, -5.416263691}
Solution
r = {11.816263691, -5.416263691}