9+(r+5)r=330

Solution for 9+(r+5)r=330 equation:

Simplifying
9 + (r + 5) * r = 330

Reorder the terms:
9 + (5 + r) * r = 330

Reorder the terms for easier multiplication:
9 + r(5 + r) = 330
9 + (5 * r + r * r) = 330
9 + (5r + r2) = 330

Solving
9 + 5r + r2 = 330

Solving for variable 'r'.

Reorder the terms:
9 + -330 + 5r + r2 = 330 + -330

Combine like terms: 9 + -330 = -321
-321 + 5r + r2 = 330 + -330

Combine like terms: 330 + -330 = 0
-321 + 5r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '321' to each side of the equation.
-321 + 5r + 321 + r2 = 0 + 321

Reorder the terms:
-321 + 321 + 5r + r2 = 0 + 321

Combine like terms: -321 + 321 = 0
0 + 5r + r2 = 0 + 321
5r + r2 = 0 + 321

Combine like terms: 0 + 321 = 321
5r + r2 = 321

The r term is 5r.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5r + 6.25 + r2 = 321 + 6.25

Reorder the terms:
6.25 + 5r + r2 = 321 + 6.25

Combine like terms: 321 + 6.25 = 327.25
6.25 + 5r + r2 = 327.25

Factor a perfect square on the left side:
(r + 2.5)(r + 2.5) = 327.25

Calculate the square root of the right side: 18.090052515

Break this problem into two subproblems by setting 
(r + 2.5) equal to 18.090052515 and -18.090052515.

Subproblem 1
r + 2.5 = 18.090052515

Simplifying
r + 2.5 = 18.090052515

Reorder the terms:
2.5 + r = 18.090052515

Solving
2.5 + r = 18.090052515

Solving for variable 'r'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + r = 18.090052515 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + r = 18.090052515 + -2.5
r = 18.090052515 + -2.5

Combine like terms: 18.090052515 + -2.5 = 15.590052515
r = 15.590052515

Simplifying
r = 15.590052515

Subproblem 2
r + 2.5 = -18.090052515

Simplifying
r + 2.5 = -18.090052515

Reorder the terms:
2.5 + r = -18.090052515

Solving
2.5 + r = -18.090052515

Solving for variable 'r'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + r = -18.090052515 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + r = -18.090052515 + -2.5
r = -18.090052515 + -2.5

Combine like terms: -18.090052515 + -2.5 = -20.590052515
r = -20.590052515

Simplifying
r = -20.590052515

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {15.590052515, -20.590052515}