16=36r-12r^2

Solution for 16=36r-12r^2 equation:

Simplifying
16 = 36r + -12r2

Solving
16 = 36r + -12r2

Solving for variable 'r'.

Reorder the terms:
16 + -36r + 12r2 = 36r + -36r + -12r2 + 12r2

Combine like terms: 36r + -36r = 0
16 + -36r + 12r2 = 0 + -12r2 + 12r2
16 + -36r + 12r2 = -12r2 + 12r2

Combine like terms: -12r2 + 12r2 = 0
16 + -36r + 12r2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + -9r + 3r2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(4 + -9r + 3r2)' equal to zero and attempt to solve:

Simplifying
4 + -9r + 3r2 = 0

Solving
4 + -9r + 3r2 = 0

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

Divide each side by '3'.
1.333333333 + -3r + r2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -3r + -1.333333333 + r2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -3r + r2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -3r + r2 = 0 + -1.333333333
-3r + r2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-3r + r2 = -1.333333333

The r term is -3r.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3r + 2.25 + r2 = -1.333333333 + 2.25

Reorder the terms:
2.25 + -3r + r2 = -1.333333333 + 2.25

Combine like terms: -1.333333333 + 2.25 = 0.916666667
2.25 + -3r + r2 = 0.916666667

Factor a perfect square on the left side:
(r + -1.5)(r + -1.5) = 0.916666667

Calculate the square root of the right side: 0.957427108

Break this problem into two subproblems by setting 
(r + -1.5) equal to 0.957427108 and -0.957427108.

Subproblem 1
r + -1.5 = 0.957427108

Simplifying
r + -1.5 = 0.957427108

Reorder the terms:
-1.5 + r = 0.957427108

Solving
-1.5 + r = 0.957427108

Solving for variable 'r'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + r = 0.957427108 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + r = 0.957427108 + 1.5
r = 0.957427108 + 1.5

Combine like terms: 0.957427108 + 1.5 = 2.457427108
r = 2.457427108

Simplifying
r = 2.457427108

Subproblem 2
r + -1.5 = -0.957427108

Simplifying
r + -1.5 = -0.957427108

Reorder the terms:
-1.5 + r = -0.957427108

Solving
-1.5 + r = -0.957427108

Solving for variable 'r'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + r = -0.957427108 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + r = -0.957427108 + 1.5
r = -0.957427108 + 1.5

Combine like terms: -0.957427108 + 1.5 = 0.542572892
r = 0.542572892

Simplifying
r = 0.542572892

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.457427108, 0.542572892}
Solution
r = {2.457427108, 0.542572892}