3r(r-6)+2=4(r+2)-21

Solution for 3r(r-6)+2=4(r+2)-21 equation:

Simplifying
3r(r + -6) + 2 = 4(r + 2) + -21

Reorder the terms:
3r(-6 + r) + 2 = 4(r + 2) + -21
(-6 * 3r + r * 3r) + 2 = 4(r + 2) + -21
(-18r + 3r2) + 2 = 4(r + 2) + -21

Reorder the terms:
2 + -18r + 3r2 = 4(r + 2) + -21

Reorder the terms:
2 + -18r + 3r2 = 4(2 + r) + -21
2 + -18r + 3r2 = (2 * 4 + r * 4) + -21
2 + -18r + 3r2 = (8 + 4r) + -21

Reorder the terms:
2 + -18r + 3r2 = 8 + -21 + 4r

Combine like terms: 8 + -21 = -13
2 + -18r + 3r2 = -13 + 4r

Solving
2 + -18r + 3r2 = -13 + 4r

Solving for variable 'r'.

Reorder the terms:
2 + 13 + -18r + -4r + 3r2 = -13 + 4r + 13 + -4r

Combine like terms: 2 + 13 = 15
15 + -18r + -4r + 3r2 = -13 + 4r + 13 + -4r

Combine like terms: -18r + -4r = -22r
15 + -22r + 3r2 = -13 + 4r + 13 + -4r

Reorder the terms:
15 + -22r + 3r2 = -13 + 13 + 4r + -4r

Combine like terms: -13 + 13 = 0
15 + -22r + 3r2 = 0 + 4r + -4r
15 + -22r + 3r2 = 4r + -4r

Combine like terms: 4r + -4r = 0
15 + -22r + 3r2 = 0

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

Divide each side by '3'.
5 + -7.333333333r + r2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -7.333333333r + -5 + r2 = 0 + -5

Reorder the terms:
5 + -5 + -7.333333333r + r2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -7.333333333r + r2 = 0 + -5
-7.333333333r + r2 = 0 + -5

Combine like terms: 0 + -5 = -5
-7.333333333r + r2 = -5

The r term is -7.333333333r.  Take half its coefficient (-3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
-7.333333333r + 13.44444445 + r2 = -5 + 13.44444445

Reorder the terms:
13.44444445 + -7.333333333r + r2 = -5 + 13.44444445

Combine like terms: -5 + 13.44444445 = 8.44444445
13.44444445 + -7.333333333r + r2 = 8.44444445

Factor a perfect square on the left side:
(r + -3.666666667)(r + -3.666666667) = 8.44444445

Calculate the square root of the right side: 2.90593263

Break this problem into two subproblems by setting 
(r + -3.666666667) equal to 2.90593263 and -2.90593263.

Subproblem 1
r + -3.666666667 = 2.90593263

Simplifying
r + -3.666666667 = 2.90593263

Reorder the terms:
-3.666666667 + r = 2.90593263

Solving
-3.666666667 + r = 2.90593263

Solving for variable 'r'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + r = 2.90593263 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + r = 2.90593263 + 3.666666667
r = 2.90593263 + 3.666666667

Combine like terms: 2.90593263 + 3.666666667 = 6.572599297
r = 6.572599297

Simplifying
r = 6.572599297

Subproblem 2
r + -3.666666667 = -2.90593263

Simplifying
r + -3.666666667 = -2.90593263

Reorder the terms:
-3.666666667 + r = -2.90593263

Solving
-3.666666667 + r = -2.90593263

Solving for variable 'r'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + r = -2.90593263 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + r = -2.90593263 + 3.666666667
r = -2.90593263 + 3.666666667

Combine like terms: -2.90593263 + 3.666666667 = 0.760734037
r = 0.760734037

Simplifying
r = 0.760734037

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {6.572599297, 0.760734037}