4r+4=-5r+3r^2

Solution for 4r+4=-5r+3r^2 equation:

Simplifying
4r + 4 = -5r + 3r2

Reorder the terms:
4 + 4r = -5r + 3r2

Solving
4 + 4r = -5r + 3r2

Solving for variable 'r'.

Combine like terms: 4r + 5r = 9r
4 + 9r + -3r2 = -5r + 3r2 + 5r + -3r2

Reorder the terms:
4 + 9r + -3r2 = -5r + 5r + 3r2 + -3r2

Combine like terms: -5r + 5r = 0
4 + 9r + -3r2 = 0 + 3r2 + -3r2
4 + 9r + -3r2 = 3r2 + -3r2

Combine like terms: 3r2 + -3r2 = 0
4 + 9r + -3r2 = 0

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

Divide each side by '-3'.
-1.333333333 + -3r + r2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -3r + 1.333333333 + r2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -3r + r2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -3r + r2 = 0 + 1.333333333
-3r + r2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-3r + r2 = 1.333333333

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 = 1.333333333 + 2.25

Reorder the terms:
2.25 + -3r + r2 = 1.333333333 + 2.25

Combine like terms: 1.333333333 + 2.25 = 3.583333333
2.25 + -3r + r2 = 3.583333333

Factor a perfect square on the left side:
(r + -1.5)(r + -1.5) = 3.583333333

Calculate the square root of the right side: 1.892969449

Break this problem into two subproblems by setting 
(r + -1.5) equal to 1.892969449 and -1.892969449.

Subproblem 1
r + -1.5 = 1.892969449

Simplifying
r + -1.5 = 1.892969449

Reorder the terms:
-1.5 + r = 1.892969449

Solving
-1.5 + r = 1.892969449

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 = 1.892969449 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + r = 1.892969449 + 1.5
r = 1.892969449 + 1.5

Combine like terms: 1.892969449 + 1.5 = 3.392969449
r = 3.392969449

Simplifying
r = 3.392969449

Subproblem 2
r + -1.5 = -1.892969449

Simplifying
r + -1.5 = -1.892969449

Reorder the terms:
-1.5 + r = -1.892969449

Solving
-1.5 + r = -1.892969449

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 = -1.892969449 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + r = -1.892969449 + 1.5
r = -1.892969449 + 1.5

Combine like terms: -1.892969449 + 1.5 = -0.392969449
r = -0.392969449

Simplifying
r = -0.392969449

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {3.392969449, -0.392969449}