5r(2r+8)=16

Solution for 5r(2r+8)=16 equation:

Simplifying
5r(2r + 8) = 16

Reorder the terms:
5r(8 + 2r) = 16
(8 * 5r + 2r * 5r) = 16
(40r + 10r2) = 16

Solving
40r + 10r2 = 16

Solving for variable 'r'.

Reorder the terms:
-16 + 40r + 10r2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 40r + 10r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 20r + 5r2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + 20r + 5r2)' equal to zero and attempt to solve:

Simplifying
-8 + 20r + 5r2 = 0

Solving
-8 + 20r + 5r2 = 0

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

Divide each side by '5'.
-1.6 + 4r + r2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 4r + 1.6 + r2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 4r + r2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 4r + r2 = 0 + 1.6
4r + r2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
4r + r2 = 1.6

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 = 1.6 + 4

Reorder the terms:
4 + 4r + r2 = 1.6 + 4

Combine like terms: 1.6 + 4 = 5.6
4 + 4r + r2 = 5.6

Factor a perfect square on the left side:
(r + 2)(r + 2) = 5.6

Calculate the square root of the right side: 2.366431913

Break this problem into two subproblems by setting 
(r + 2) equal to 2.366431913 and -2.366431913.

Subproblem 1
r + 2 = 2.366431913

Simplifying
r + 2 = 2.366431913

Reorder the terms:
2 + r = 2.366431913

Solving
2 + r = 2.366431913

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 = 2.366431913 + -2

Combine like terms: 2 + -2 = 0
0 + r = 2.366431913 + -2
r = 2.366431913 + -2

Combine like terms: 2.366431913 + -2 = 0.366431913
r = 0.366431913

Simplifying
r = 0.366431913

Subproblem 2
r + 2 = -2.366431913

Simplifying
r + 2 = -2.366431913

Reorder the terms:
2 + r = -2.366431913

Solving
2 + r = -2.366431913

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 = -2.366431913 + -2

Combine like terms: 2 + -2 = 0
0 + r = -2.366431913 + -2
r = -2.366431913 + -2

Combine like terms: -2.366431913 + -2 = -4.366431913
r = -4.366431913

Simplifying
r = -4.366431913

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.366431913, -4.366431913}
Solution
r = {0.366431913, -4.366431913}