4(r+2)r=26

Solution for 4(r+2)r=26 equation:

Simplifying
4(r + 2) * r = 26

Reorder the terms:
4(2 + r) * r = 26

Reorder the terms for easier multiplication:
4r(2 + r) = 26
(2 * 4r + r * 4r) = 26
(8r + 4r2) = 26

Solving
8r + 4r2 = 26

Solving for variable 'r'.

Reorder the terms:
-26 + 8r + 4r2 = 26 + -26

Combine like terms: 26 + -26 = 0
-26 + 8r + 4r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + 4r + 2r2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-13 + 4r + 2r2)' equal to zero and attempt to solve:

Simplifying
-13 + 4r + 2r2 = 0

Solving
-13 + 4r + 2r2 = 0

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

Divide each side by '2'.
-6.5 + 2r + r2 = 0

Move the constant term to the right:

Add '6.5' to each side of the equation.
-6.5 + 2r + 6.5 + r2 = 0 + 6.5

Reorder the terms:
-6.5 + 6.5 + 2r + r2 = 0 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + 2r + r2 = 0 + 6.5
2r + r2 = 0 + 6.5

Combine like terms: 0 + 6.5 = 6.5
2r + r2 = 6.5

The r term is 2r.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2r + 1 + r2 = 6.5 + 1

Reorder the terms:
1 + 2r + r2 = 6.5 + 1

Combine like terms: 6.5 + 1 = 7.5
1 + 2r + r2 = 7.5

Factor a perfect square on the left side:
(r + 1)(r + 1) = 7.5

Calculate the square root of the right side: 2.738612788

Break this problem into two subproblems by setting 
(r + 1) equal to 2.738612788 and -2.738612788.

Subproblem 1
r + 1 = 2.738612788

Simplifying
r + 1 = 2.738612788

Reorder the terms:
1 + r = 2.738612788

Solving
1 + r = 2.738612788

Solving for variable 'r'.

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

Add '-1' to each side of the equation.
1 + -1 + r = 2.738612788 + -1

Combine like terms: 1 + -1 = 0
0 + r = 2.738612788 + -1
r = 2.738612788 + -1

Combine like terms: 2.738612788 + -1 = 1.738612788
r = 1.738612788

Simplifying
r = 1.738612788

Subproblem 2
r + 1 = -2.738612788

Simplifying
r + 1 = -2.738612788

Reorder the terms:
1 + r = -2.738612788

Solving
1 + r = -2.738612788

Solving for variable 'r'.

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

Add '-1' to each side of the equation.
1 + -1 + r = -2.738612788 + -1

Combine like terms: 1 + -1 = 0
0 + r = -2.738612788 + -1
r = -2.738612788 + -1

Combine like terms: -2.738612788 + -1 = -3.738612788
r = -3.738612788

Simplifying
r = -3.738612788

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.738612788, -3.738612788}
Solution
r = {1.738612788, -3.738612788}