57.6=144-48r+4r^2

Solution for 57.6=144-48r+4r^2 equation:

Simplifying
57.6 = 144 + -48r + 4r2

Solving
57.6 = 144 + -48r + 4r2

Solving for variable 'r'.

Combine like terms: 57.6 + -144 = -86.4
-86.4 + 48r + -4r2 = 144 + -48r + 4r2 + -144 + 48r + -4r2

Reorder the terms:
-86.4 + 48r + -4r2 = 144 + -144 + -48r + 48r + 4r2 + -4r2

Combine like terms: 144 + -144 = 0
-86.4 + 48r + -4r2 = 0 + -48r + 48r + 4r2 + -4r2
-86.4 + 48r + -4r2 = -48r + 48r + 4r2 + -4r2

Combine like terms: -48r + 48r = 0
-86.4 + 48r + -4r2 = 0 + 4r2 + -4r2
-86.4 + 48r + -4r2 = 4r2 + -4r2

Combine like terms: 4r2 + -4r2 = 0
-86.4 + 48r + -4r2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
21.6 + -12r + r2 = 0

Move the constant term to the right:

Add '-21.6' to each side of the equation.
21.6 + -12r + -21.6 + r2 = 0 + -21.6

Reorder the terms:
21.6 + -21.6 + -12r + r2 = 0 + -21.6

Combine like terms: 21.6 + -21.6 = 0.0
0.0 + -12r + r2 = 0 + -21.6
-12r + r2 = 0 + -21.6

Combine like terms: 0 + -21.6 = -21.6
-12r + r2 = -21.6

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 = -21.6 + 36

Reorder the terms:
36 + -12r + r2 = -21.6 + 36

Combine like terms: -21.6 + 36 = 14.4
36 + -12r + r2 = 14.4

Factor a perfect square on the left side:
(r + -6)(r + -6) = 14.4

Calculate the square root of the right side: 3.794733192

Break this problem into two subproblems by setting 
(r + -6) equal to 3.794733192 and -3.794733192.

Subproblem 1
r + -6 = 3.794733192

Simplifying
r + -6 = 3.794733192

Reorder the terms:
-6 + r = 3.794733192

Solving
-6 + r = 3.794733192

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 = 3.794733192 + 6

Combine like terms: -6 + 6 = 0
0 + r = 3.794733192 + 6
r = 3.794733192 + 6

Combine like terms: 3.794733192 + 6 = 9.794733192
r = 9.794733192

Simplifying
r = 9.794733192

Subproblem 2
r + -6 = -3.794733192

Simplifying
r + -6 = -3.794733192

Reorder the terms:
-6 + r = -3.794733192

Solving
-6 + r = -3.794733192

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 = -3.794733192 + 6

Combine like terms: -6 + 6 = 0
0 + r = -3.794733192 + 6
r = -3.794733192 + 6

Combine like terms: -3.794733192 + 6 = 2.205266808
r = 2.205266808

Simplifying
r = 2.205266808

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {9.794733192, 2.205266808}