-3r^2+2r+7-9+4r+r^2=

Solution for -3r^2+2r+7-9+4r+r^2= equation:

Simplifying
-3r2 + 2r + 7 + -9 + 4r + r2 = 0

Reorder the terms:
7 + -9 + 2r + 4r + -3r2 + r2 = 0

Combine like terms: 7 + -9 = -2
-2 + 2r + 4r + -3r2 + r2 = 0

Combine like terms: 2r + 4r = 6r
-2 + 6r + -3r2 + r2 = 0

Combine like terms: -3r2 + r2 = -2r2
-2 + 6r + -2r2 = 0

Solving
-2 + 6r + -2r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 3r + -1r2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 3r + -1r2)' equal to zero and attempt to solve:

Simplifying
-1 + 3r + -1r2 = 0

Solving
-1 + 3r + -1r2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
1 + -3r + r2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3r + -1 + r2 = 0 + -1

Reorder the terms:
1 + -1 + -3r + r2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3r + r2 = 0 + -1
-3r + r2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3r + r2 = -1

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 + 2.25

Reorder the terms:
2.25 + -3r + r2 = -1 + 2.25

Combine like terms: -1 + 2.25 = 1.25
2.25 + -3r + r2 = 1.25

Factor a perfect square on the left side:
(r + -1.5)(r + -1.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(r + -1.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
r + -1.5 = 1.118033989

Simplifying
r + -1.5 = 1.118033989

Reorder the terms:
-1.5 + r = 1.118033989

Solving
-1.5 + r = 1.118033989

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 = 1.118033989 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + r = 1.118033989 + 1.5
r = 1.118033989 + 1.5

Combine like terms: 1.118033989 + 1.5 = 2.618033989
r = 2.618033989

Simplifying
r = 2.618033989

Subproblem 2
r + -1.5 = -1.118033989

Simplifying
r + -1.5 = -1.118033989

Reorder the terms:
-1.5 + r = -1.118033989

Solving
-1.5 + r = -1.118033989

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 = -1.118033989 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + r = -1.118033989 + 1.5
r = -1.118033989 + 1.5

Combine like terms: -1.118033989 + 1.5 = 0.381966011
r = 0.381966011

Simplifying
r = 0.381966011

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.618033989, 0.381966011}
Solution
r = {2.618033989, 0.381966011}