(b+3)(b)=26

Solution for (b+3)(b)=26 equation:

Simplifying
(b + 3)(b) = 26

Reorder the terms:
(3 + b)(b) = 26

Reorder the terms for easier multiplication:
b(3 + b) = 26
(3 * b + b * b) = 26
(3b + b2) = 26

Solving
3b + b2 = 26

Solving for variable 'b'.

Reorder the terms:
-26 + 3b + b2 = 26 + -26

Combine like terms: 26 + -26 = 0
-26 + 3b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + 3b + 26 + b2 = 0 + 26

Reorder the terms:
-26 + 26 + 3b + b2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + 3b + b2 = 0 + 26
3b + b2 = 0 + 26

Combine like terms: 0 + 26 = 26
3b + b2 = 26

The b term is 3b.  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.
3b + 2.25 + b2 = 26 + 2.25

Reorder the terms:
2.25 + 3b + b2 = 26 + 2.25

Combine like terms: 26 + 2.25 = 28.25
2.25 + 3b + b2 = 28.25

Factor a perfect square on the left side:
(b + 1.5)(b + 1.5) = 28.25

Calculate the square root of the right side: 5.315072906

Break this problem into two subproblems by setting 
(b + 1.5) equal to 5.315072906 and -5.315072906.

Subproblem 1
b + 1.5 = 5.315072906

Simplifying
b + 1.5 = 5.315072906

Reorder the terms:
1.5 + b = 5.315072906

Solving
1.5 + b = 5.315072906

Solving for variable 'b'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + b = 5.315072906 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + b = 5.315072906 + -1.5
b = 5.315072906 + -1.5

Combine like terms: 5.315072906 + -1.5 = 3.815072906
b = 3.815072906

Simplifying
b = 3.815072906

Subproblem 2
b + 1.5 = -5.315072906

Simplifying
b + 1.5 = -5.315072906

Reorder the terms:
1.5 + b = -5.315072906

Solving
1.5 + b = -5.315072906

Solving for variable 'b'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + b = -5.315072906 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + b = -5.315072906 + -1.5
b = -5.315072906 + -1.5

Combine like terms: -5.315072906 + -1.5 = -6.815072906
b = -6.815072906

Simplifying
b = -6.815072906

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {3.815072906, -6.815072906}