3r-5r(r-1)-10r=-43

Solution for 3r-5r(r-1)-10r=-43 equation:

Simplifying
3r + -5r(r + -1) + -10r = -43

Reorder the terms:
3r + -5r(-1 + r) + -10r = -43
3r + (-1 * -5r + r * -5r) + -10r = -43
3r + (5r + -5r2) + -10r = -43

Reorder the terms:
3r + 5r + -10r + -5r2 = -43

Combine like terms: 3r + 5r = 8r
8r + -10r + -5r2 = -43

Combine like terms: 8r + -10r = -2r
-2r + -5r2 = -43

Solving
-2r + -5r2 = -43

Solving for variable 'r'.

Reorder the terms:
43 + -2r + -5r2 = -43 + 43

Combine like terms: -43 + 43 = 0
43 + -2r + -5r2 = 0

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

Divide each side by '-5'.
-8.6 + 0.4r + r2 = 0

Move the constant term to the right:

Add '8.6' to each side of the equation.
-8.6 + 0.4r + 8.6 + r2 = 0 + 8.6

Reorder the terms:
-8.6 + 8.6 + 0.4r + r2 = 0 + 8.6

Combine like terms: -8.6 + 8.6 = 0.0
0.0 + 0.4r + r2 = 0 + 8.6
0.4r + r2 = 0 + 8.6

Combine like terms: 0 + 8.6 = 8.6
0.4r + r2 = 8.6

The r term is 0.4r.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4r + 0.04 + r2 = 8.6 + 0.04

Reorder the terms:
0.04 + 0.4r + r2 = 8.6 + 0.04

Combine like terms: 8.6 + 0.04 = 8.64
0.04 + 0.4r + r2 = 8.64

Factor a perfect square on the left side:
(r + 0.2)(r + 0.2) = 8.64

Calculate the square root of the right side: 2.939387691

Break this problem into two subproblems by setting 
(r + 0.2) equal to 2.939387691 and -2.939387691.

Subproblem 1
r + 0.2 = 2.939387691

Simplifying
r + 0.2 = 2.939387691

Reorder the terms:
0.2 + r = 2.939387691

Solving
0.2 + r = 2.939387691

Solving for variable 'r'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + r = 2.939387691 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + r = 2.939387691 + -0.2
r = 2.939387691 + -0.2

Combine like terms: 2.939387691 + -0.2 = 2.739387691
r = 2.739387691

Simplifying
r = 2.739387691

Subproblem 2
r + 0.2 = -2.939387691

Simplifying
r + 0.2 = -2.939387691

Reorder the terms:
0.2 + r = -2.939387691

Solving
0.2 + r = -2.939387691

Solving for variable 'r'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + r = -2.939387691 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + r = -2.939387691 + -0.2
r = -2.939387691 + -0.2

Combine like terms: -2.939387691 + -0.2 = -3.139387691
r = -3.139387691

Simplifying
r = -3.139387691

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.739387691, -3.139387691}