44r+16r(-20r)-3r+(-43r)=36

Solution for 44r+16r(-20r)-3r+(-43r)=36 equation:

Simplifying
44r + 16r(-20r) + -3r + (-43r) = 36

Remove parenthesis around (-20r)
44r + 16r * -20r + -3r + (-43r) = 36

Reorder the terms for easier multiplication:
44r + 16 * -20r * r + -3r + (-43r) = 36

Multiply 16 * -20
44r + -320r * r + -3r + (-43r) = 36

Multiply r * r
44r + -320r2 + -3r + (-43r) = 36

Reorder the terms:
44r + -3r + (-43r) + -320r2 = 36

Combine like terms: 44r + -3r = 41r
41r + (-43r) + -320r2 = 36

Combine like terms: 41r + (-43r) = -2r
-2r + -320r2 = 36

Solving
-2r + -320r2 = 36

Solving for variable 'r'.

Reorder the terms:
-36 + -2r + -320r2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + -2r + -320r2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(18 + r + 160r2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(18 + r + 160r2)' equal to zero and attempt to solve:

Simplifying
18 + r + 160r2 = 0

Solving
18 + r + 160r2 = 0

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

Divide each side by '160'.
0.1125 + 0.00625r + r2 = 0.0

Move the constant term to the right:

Add '-0.1125' to each side of the equation.
0.1125 + 0.00625r + -0.1125 + r2 = 0.0 + -0.1125

Reorder the terms:
0.1125 + -0.1125 + 0.00625r + r2 = 0.0 + -0.1125

Combine like terms: 0.1125 + -0.1125 = 0.0000
0.0000 + 0.00625r + r2 = 0.0 + -0.1125
0.00625r + r2 = 0.0 + -0.1125

Combine like terms: 0.0 + -0.1125 = -0.1125
0.00625r + r2 = -0.1125

The r term is r.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.00625r + 0.25 + r2 = -0.1125 + 0.25

Reorder the terms:
0.25 + 0.00625r + r2 = -0.1125 + 0.25

Combine like terms: -0.1125 + 0.25 = 0.1375
0.25 + 0.00625r + r2 = 0.1375

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = 0.1375

Calculate the square root of the right side: 0.370809924

Break this problem into two subproblems by setting 
(r + 0.5) equal to 0.370809924 and -0.370809924.

Subproblem 1
r + 0.5 = 0.370809924

Simplifying
r + 0.5 = 0.370809924

Reorder the terms:
0.5 + r = 0.370809924

Solving
0.5 + r = 0.370809924

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = 0.370809924 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = 0.370809924 + -0.5
r = 0.370809924 + -0.5

Combine like terms: 0.370809924 + -0.5 = -0.129190076
r = -0.129190076

Simplifying
r = -0.129190076

Subproblem 2
r + 0.5 = -0.370809924

Simplifying
r + 0.5 = -0.370809924

Reorder the terms:
0.5 + r = -0.370809924

Solving
0.5 + r = -0.370809924

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = -0.370809924 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = -0.370809924 + -0.5
r = -0.370809924 + -0.5

Combine like terms: -0.370809924 + -0.5 = -0.870809924
r = -0.870809924

Simplifying
r = -0.870809924

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-0.129190076, -0.870809924}
Solution
r = {-0.129190076, -0.870809924}