6-2r+1=3r-5r(r-2)

Solution for 6-2r+1=3r-5r(r-2) equation:

Simplifying
6 + -2r + 1 = 3r + -5r(r + -2)

Reorder the terms:
6 + 1 + -2r = 3r + -5r(r + -2)

Combine like terms: 6 + 1 = 7
7 + -2r = 3r + -5r(r + -2)

Reorder the terms:
7 + -2r = 3r + -5r(-2 + r)
7 + -2r = 3r + (-2 * -5r + r * -5r)
7 + -2r = 3r + (10r + -5r2)

Combine like terms: 3r + 10r = 13r
7 + -2r = 13r + -5r2

Solving
7 + -2r = 13r + -5r2

Solving for variable 'r'.

Combine like terms: -2r + -13r = -15r
7 + -15r + 5r2 = 13r + -5r2 + -13r + 5r2

Reorder the terms:
7 + -15r + 5r2 = 13r + -13r + -5r2 + 5r2

Combine like terms: 13r + -13r = 0
7 + -15r + 5r2 = 0 + -5r2 + 5r2
7 + -15r + 5r2 = -5r2 + 5r2

Combine like terms: -5r2 + 5r2 = 0
7 + -15r + 5r2 = 0

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

Divide each side by '5'.
1.4 + -3r + r2 = 0

Move the constant term to the right:

Add '-1.4' to each side of the equation.
1.4 + -3r + -1.4 + r2 = 0 + -1.4

Reorder the terms:
1.4 + -1.4 + -3r + r2 = 0 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + -3r + r2 = 0 + -1.4
-3r + r2 = 0 + -1.4

Combine like terms: 0 + -1.4 = -1.4
-3r + r2 = -1.4

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 = -1.4 + 2.25

Reorder the terms:
2.25 + -3r + r2 = -1.4 + 2.25

Combine like terms: -1.4 + 2.25 = 0.85
2.25 + -3r + r2 = 0.85

Factor a perfect square on the left side:
(r + -1.5)(r + -1.5) = 0.85

Calculate the square root of the right side: 0.921954446

Break this problem into two subproblems by setting 
(r + -1.5) equal to 0.921954446 and -0.921954446.

Subproblem 1
r + -1.5 = 0.921954446

Simplifying
r + -1.5 = 0.921954446

Reorder the terms:
-1.5 + r = 0.921954446

Solving
-1.5 + r = 0.921954446

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 = 0.921954446 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + r = 0.921954446 + 1.5
r = 0.921954446 + 1.5

Combine like terms: 0.921954446 + 1.5 = 2.421954446
r = 2.421954446

Simplifying
r = 2.421954446

Subproblem 2
r + -1.5 = -0.921954446

Simplifying
r + -1.5 = -0.921954446

Reorder the terms:
-1.5 + r = -0.921954446

Solving
-1.5 + r = -0.921954446

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 = -0.921954446 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + r = -0.921954446 + 1.5
r = -0.921954446 + 1.5

Combine like terms: -0.921954446 + 1.5 = 0.578045554
r = 0.578045554

Simplifying
r = 0.578045554

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.421954446, 0.578045554}