r(r-12)=36

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Solution for r(r-12)=36 equation: 


Simplifying
r(r + -12) = 36

Reorder the terms:
r(-12 + r) = 36
(-12 * r + r * r) = 36
(-12r + r2) = 36

Solving
-12r + r2 = 36

Solving for variable 'r'.

Reorder the terms:
-36 + -12r + r2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + -12r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -12r + 36 + r2 = 0 + 36

Reorder the terms:
-36 + 36 + -12r + r2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -12r + r2 = 0 + 36
-12r + r2 = 0 + 36

Combine like terms: 0 + 36 = 36
-12r + r2 = 36

The r term is -12r.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12r + 36 + r2 = 36 + 36

Reorder the terms:
36 + -12r + r2 = 36 + 36

Combine like terms: 36 + 36 = 72
36 + -12r + r2 = 72

Factor a perfect square on the left side:
(r + -6)(r + -6) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(r + -6) equal to 8.485281374 and -8.485281374.


Subproblem 1
r + -6 = 8.485281374

Simplifying
r + -6 = 8.485281374

Reorder the terms:
-6 + r = 8.485281374

Solving
-6 + r = 8.485281374

Solving for variable 'r'.

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

Add '6' to each side of the equation.
-6 + 6 + r = 8.485281374 + 6

Combine like terms: -6 + 6 = 0
0 + r = 8.485281374 + 6
r = 8.485281374 + 6

Combine like terms: 8.485281374 + 6 = 14.485281374
r = 14.485281374

Simplifying
r = 14.485281374


Subproblem 2
r + -6 = -8.485281374

Simplifying
r + -6 = -8.485281374

Reorder the terms:
-6 + r = -8.485281374

Solving
-6 + r = -8.485281374

Solving for variable 'r'.

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

Add '6' to each side of the equation.
-6 + 6 + r = -8.485281374 + 6

Combine like terms: -6 + 6 = 0
0 + r = -8.485281374 + 6
r = -8.485281374 + 6

Combine like terms: -8.485281374 + 6 = -2.485281374
r = -2.485281374

Simplifying
r = -2.485281374


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {14.485281374, -2.485281374}

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