4r(r-5)-16r=10

Solution for 4r(r-5)-16r=10 equation:

Simplifying
4r(r + -5) + -16r = 10

Reorder the terms:
4r(-5 + r) + -16r = 10
(-5 * 4r + r * 4r) + -16r = 10
(-20r + 4r2) + -16r = 10

Reorder the terms:
-20r + -16r + 4r2 = 10

Combine like terms: -20r + -16r = -36r
-36r + 4r2 = 10

Solving
-36r + 4r2 = 10

Solving for variable 'r'.

Reorder the terms:
-10 + -36r + 4r2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -36r + 4r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -18r + 2r2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -18r + 2r2)' equal to zero and attempt to solve:

Simplifying
-5 + -18r + 2r2 = 0

Solving
-5 + -18r + 2r2 = 0

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

Divide each side by '2'.
-2.5 + -9r + r2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -9r + 2.5 + r2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -9r + r2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -9r + r2 = 0 + 2.5
-9r + r2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-9r + r2 = 2.5

The r term is -9r.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9r + 20.25 + r2 = 2.5 + 20.25

Reorder the terms:
20.25 + -9r + r2 = 2.5 + 20.25

Combine like terms: 2.5 + 20.25 = 22.75
20.25 + -9r + r2 = 22.75

Factor a perfect square on the left side:
(r + -4.5)(r + -4.5) = 22.75

Calculate the square root of the right side: 4.769696007

Break this problem into two subproblems by setting 
(r + -4.5) equal to 4.769696007 and -4.769696007.

Subproblem 1
r + -4.5 = 4.769696007

Simplifying
r + -4.5 = 4.769696007

Reorder the terms:
-4.5 + r = 4.769696007

Solving
-4.5 + r = 4.769696007

Solving for variable 'r'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + r = 4.769696007 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + r = 4.769696007 + 4.5
r = 4.769696007 + 4.5

Combine like terms: 4.769696007 + 4.5 = 9.269696007
r = 9.269696007

Simplifying
r = 9.269696007

Subproblem 2
r + -4.5 = -4.769696007

Simplifying
r + -4.5 = -4.769696007

Reorder the terms:
-4.5 + r = -4.769696007

Solving
-4.5 + r = -4.769696007

Solving for variable 'r'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + r = -4.769696007 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + r = -4.769696007 + 4.5
r = -4.769696007 + 4.5

Combine like terms: -4.769696007 + 4.5 = -0.269696007
r = -0.269696007

Simplifying
r = -0.269696007

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {9.269696007, -0.269696007}
Solution
r = {9.269696007, -0.269696007}