(8r-1)(5+2r)=(4r+5)

Solution for (8r-1)(5+2r)=(4r+5) equation:

Simplifying
(8r + -1)(5 + 2r) = (4r + 5)

Reorder the terms:
(-1 + 8r)(5 + 2r) = (4r + 5)

Multiply (-1 + 8r) * (5 + 2r)
(-1(5 + 2r) + 8r * (5 + 2r)) = (4r + 5)
((5 * -1 + 2r * -1) + 8r * (5 + 2r)) = (4r + 5)
((-5 + -2r) + 8r * (5 + 2r)) = (4r + 5)
(-5 + -2r + (5 * 8r + 2r * 8r)) = (4r + 5)
(-5 + -2r + (40r + 16r2)) = (4r + 5)

Combine like terms: -2r + 40r = 38r
(-5 + 38r + 16r2) = (4r + 5)

Reorder the terms:
-5 + 38r + 16r2 = (5 + 4r)

Remove parenthesis around (5 + 4r)
-5 + 38r + 16r2 = 5 + 4r

Solving
-5 + 38r + 16r2 = 5 + 4r

Solving for variable 'r'.

Reorder the terms:
-5 + -5 + 38r + -4r + 16r2 = 5 + 4r + -5 + -4r

Combine like terms: -5 + -5 = -10
-10 + 38r + -4r + 16r2 = 5 + 4r + -5 + -4r

Combine like terms: 38r + -4r = 34r
-10 + 34r + 16r2 = 5 + 4r + -5 + -4r

Reorder the terms:
-10 + 34r + 16r2 = 5 + -5 + 4r + -4r

Combine like terms: 5 + -5 = 0
-10 + 34r + 16r2 = 0 + 4r + -4r
-10 + 34r + 16r2 = 4r + -4r

Combine like terms: 4r + -4r = 0
-10 + 34r + 16r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 17r + 8r2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + 17r + 8r2)' equal to zero and attempt to solve:

Simplifying
-5 + 17r + 8r2 = 0

Solving
-5 + 17r + 8r2 = 0

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

Divide each side by '8'.
-0.625 + 2.125r + r2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + 2.125r + 0.625 + r2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + 2.125r + r2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + 2.125r + r2 = 0 + 0.625
2.125r + r2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
2.125r + r2 = 0.625

The r term is 2.125r.  Take half its coefficient (1.0625).
Square it (1.12890625) and add it to both sides.

Add '1.12890625' to each side of the equation.
2.125r + 1.12890625 + r2 = 0.625 + 1.12890625

Reorder the terms:
1.12890625 + 2.125r + r2 = 0.625 + 1.12890625

Combine like terms: 0.625 + 1.12890625 = 1.75390625
1.12890625 + 2.125r + r2 = 1.75390625

Factor a perfect square on the left side:
(r + 1.0625)(r + 1.0625) = 1.75390625

Calculate the square root of the right side: 1.324351256

Break this problem into two subproblems by setting 
(r + 1.0625) equal to 1.324351256 and -1.324351256.

Subproblem 1
r + 1.0625 = 1.324351256

Simplifying
r + 1.0625 = 1.324351256

Reorder the terms:
1.0625 + r = 1.324351256

Solving
1.0625 + r = 1.324351256

Solving for variable 'r'.

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

Add '-1.0625' to each side of the equation.
1.0625 + -1.0625 + r = 1.324351256 + -1.0625

Combine like terms: 1.0625 + -1.0625 = 0.0000
0.0000 + r = 1.324351256 + -1.0625
r = 1.324351256 + -1.0625

Combine like terms: 1.324351256 + -1.0625 = 0.261851256
r = 0.261851256

Simplifying
r = 0.261851256

Subproblem 2
r + 1.0625 = -1.324351256

Simplifying
r + 1.0625 = -1.324351256

Reorder the terms:
1.0625 + r = -1.324351256

Solving
1.0625 + r = -1.324351256

Solving for variable 'r'.

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

Add '-1.0625' to each side of the equation.
1.0625 + -1.0625 + r = -1.324351256 + -1.0625

Combine like terms: 1.0625 + -1.0625 = 0.0000
0.0000 + r = -1.324351256 + -1.0625
r = -1.324351256 + -1.0625

Combine like terms: -1.324351256 + -1.0625 = -2.386851256
r = -2.386851256

Simplifying
r = -2.386851256

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.261851256, -2.386851256}
Solution
r = {0.261851256, -2.386851256}