5(r+2)+5(r-2)=200(r+2)(r-2)

Solution for 5(r+2)+5(r-2)=200(r+2)(r-2) equation:

Simplifying
5(r + 2) + 5(r + -2) = 200(r + 2)(r + -2)

Reorder the terms:
5(2 + r) + 5(r + -2) = 200(r + 2)(r + -2)
(2 * 5 + r * 5) + 5(r + -2) = 200(r + 2)(r + -2)
(10 + 5r) + 5(r + -2) = 200(r + 2)(r + -2)

Reorder the terms:
10 + 5r + 5(-2 + r) = 200(r + 2)(r + -2)
10 + 5r + (-2 * 5 + r * 5) = 200(r + 2)(r + -2)
10 + 5r + (-10 + 5r) = 200(r + 2)(r + -2)

Reorder the terms:
10 + -10 + 5r + 5r = 200(r + 2)(r + -2)

Combine like terms: 10 + -10 = 0
0 + 5r + 5r = 200(r + 2)(r + -2)
5r + 5r = 200(r + 2)(r + -2)

Combine like terms: 5r + 5r = 10r
10r = 200(r + 2)(r + -2)

Reorder the terms:
10r = 200(2 + r)(r + -2)

Reorder the terms:
10r = 200(2 + r)(-2 + r)

Multiply (2 + r) * (-2 + r)
10r = 200(2(-2 + r) + r(-2 + r))
10r = 200((-2 * 2 + r * 2) + r(-2 + r))
10r = 200((-4 + 2r) + r(-2 + r))
10r = 200(-4 + 2r + (-2 * r + r * r))
10r = 200(-4 + 2r + (-2r + r2))

Combine like terms: 2r + -2r = 0
10r = 200(-4 + 0 + r2)
10r = 200(-4 + r2)
10r = (-4 * 200 + r2 * 200)
10r = (-800 + 200r2)

Solving
10r = -800 + 200r2

Solving for variable 'r'.

Reorder the terms:
800 + 10r + -200r2 = -800 + 200r2 + 800 + -200r2

Reorder the terms:
800 + 10r + -200r2 = -800 + 800 + 200r2 + -200r2

Combine like terms: -800 + 800 = 0
800 + 10r + -200r2 = 0 + 200r2 + -200r2
800 + 10r + -200r2 = 200r2 + -200r2

Combine like terms: 200r2 + -200r2 = 0
800 + 10r + -200r2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(80 + r + -20r2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(80 + r + -20r2)' equal to zero and attempt to solve:

Simplifying
80 + r + -20r2 = 0

Solving
80 + r + -20r2 = 0

Begin completing the square.  Divide all terms by
-20 the coefficient of the squared term: 

Divide each side by '-20'.
-4 + -0.05r + r2 = 0.0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -0.05r + 4 + r2 = 0.0 + 4

Reorder the terms:
-4 + 4 + -0.05r + r2 = 0.0 + 4

Combine like terms: -4 + 4 = 0
0 + -0.05r + r2 = 0.0 + 4
-0.05r + r2 = 0.0 + 4

Combine like terms: 0.0 + 4 = 4
-0.05r + r2 = 4

The r term is r.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.05r + 0.25 + r2 = 4 + 0.25

Reorder the terms:
0.25 + -0.05r + r2 = 4 + 0.25

Combine like terms: 4 + 0.25 = 4.25
0.25 + -0.05r + r2 = 4.25

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(r + 0.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
r + 0.5 = 2.061552813

Simplifying
r + 0.5 = 2.061552813

Reorder the terms:
0.5 + r = 2.061552813

Solving
0.5 + r = 2.061552813

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = 2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = 2.061552813 + -0.5
r = 2.061552813 + -0.5

Combine like terms: 2.061552813 + -0.5 = 1.561552813
r = 1.561552813

Simplifying
r = 1.561552813

Subproblem 2
r + 0.5 = -2.061552813

Simplifying
r + 0.5 = -2.061552813

Reorder the terms:
0.5 + r = -2.061552813

Solving
0.5 + r = -2.061552813

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = -2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = -2.061552813 + -0.5
r = -2.061552813 + -0.5

Combine like terms: -2.061552813 + -0.5 = -2.561552813
r = -2.561552813

Simplifying
r = -2.561552813

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.561552813, -2.561552813}
Solution
r = {1.561552813, -2.561552813}