3(r-5)(r+5)=10r+50+10r-50

Solution for 3(r-5)(r+5)=10r+50+10r-50 equation:

Simplifying
3(r + -5)(r + 5) = 10r + 50 + 10r + -50

Reorder the terms:
3(-5 + r)(r + 5) = 10r + 50 + 10r + -50

Reorder the terms:
3(-5 + r)(5 + r) = 10r + 50 + 10r + -50

Multiply (-5 + r) * (5 + r)
3(-5(5 + r) + r(5 + r)) = 10r + 50 + 10r + -50
3((5 * -5 + r * -5) + r(5 + r)) = 10r + 50 + 10r + -50
3((-25 + -5r) + r(5 + r)) = 10r + 50 + 10r + -50
3(-25 + -5r + (5 * r + r * r)) = 10r + 50 + 10r + -50
3(-25 + -5r + (5r + r2)) = 10r + 50 + 10r + -50

Combine like terms: -5r + 5r = 0
3(-25 + 0 + r2) = 10r + 50 + 10r + -50
3(-25 + r2) = 10r + 50 + 10r + -50
(-25 * 3 + r2 * 3) = 10r + 50 + 10r + -50
(-75 + 3r2) = 10r + 50 + 10r + -50

Reorder the terms:
-75 + 3r2 = 50 + -50 + 10r + 10r

Combine like terms: 50 + -50 = 0
-75 + 3r2 = 0 + 10r + 10r
-75 + 3r2 = 10r + 10r

Combine like terms: 10r + 10r = 20r
-75 + 3r2 = 20r

Solving
-75 + 3r2 = 20r

Solving for variable 'r'.

Reorder the terms:
-75 + -20r + 3r2 = 20r + -20r

Combine like terms: 20r + -20r = 0
-75 + -20r + 3r2 = 0

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

Divide each side by '3'.
-25 + -6.666666667r + r2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -6.666666667r + 25 + r2 = 0 + 25

Reorder the terms:
-25 + 25 + -6.666666667r + r2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -6.666666667r + r2 = 0 + 25
-6.666666667r + r2 = 0 + 25

Combine like terms: 0 + 25 = 25
-6.666666667r + r2 = 25

The r term is -6.666666667r.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667r + 11.11111112 + r2 = 25 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667r + r2 = 25 + 11.11111112

Combine like terms: 25 + 11.11111112 = 36.11111112
11.11111112 + -6.666666667r + r2 = 36.11111112

Factor a perfect square on the left side:
(r + -3.333333334)(r + -3.333333334) = 36.11111112

Calculate the square root of the right side: 6.009252127

Break this problem into two subproblems by setting 
(r + -3.333333334) equal to 6.009252127 and -6.009252127.

Subproblem 1
r + -3.333333334 = 6.009252127

Simplifying
r + -3.333333334 = 6.009252127

Reorder the terms:
-3.333333334 + r = 6.009252127

Solving
-3.333333334 + r = 6.009252127

Solving for variable 'r'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + r = 6.009252127 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + r = 6.009252127 + 3.333333334
r = 6.009252127 + 3.333333334

Combine like terms: 6.009252127 + 3.333333334 = 9.342585461
r = 9.342585461

Simplifying
r = 9.342585461

Subproblem 2
r + -3.333333334 = -6.009252127

Simplifying
r + -3.333333334 = -6.009252127

Reorder the terms:
-3.333333334 + r = -6.009252127

Solving
-3.333333334 + r = -6.009252127

Solving for variable 'r'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + r = -6.009252127 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + r = -6.009252127 + 3.333333334
r = -6.009252127 + 3.333333334

Combine like terms: -6.009252127 + 3.333333334 = -2.675918793
r = -2.675918793

Simplifying
r = -2.675918793

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {9.342585461, -2.675918793}