2+5=(3b+9)b

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Solution for 2+5=(3b+9)b equation: 


Simplifying
2 + 5 = (3b + 9) * b

Combine like terms: 2 + 5 = 7
7 = (3b + 9) * b

Reorder the terms:
7 = (9 + 3b) * b

Reorder the terms for easier multiplication:
7 = b(9 + 3b)
7 = (9 * b + 3b * b)
7 = (9b + 3b2)

Solving
7 = 9b + 3b2

Solving for variable 'b'.

Reorder the terms:
7 + -9b + -3b2 = 9b + -9b + 3b2 + -3b2

Combine like terms: 9b + -9b = 0
7 + -9b + -3b2 = 0 + 3b2 + -3b2
7 + -9b + -3b2 = 3b2 + -3b2

Combine like terms: 3b2 + -3b2 = 0
7 + -9b + -3b2 = 0

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

Divide each side by '-3'.
-2.333333333 + 3b + b2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + 3b + 2.333333333 + b2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + 3b + b2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + 3b + b2 = 0 + 2.333333333
3b + b2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
3b + b2 = 2.333333333

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 = 2.333333333 + 2.25

Reorder the terms:
2.25 + 3b + b2 = 2.333333333 + 2.25

Combine like terms: 2.333333333 + 2.25 = 4.583333333
2.25 + 3b + b2 = 4.583333333

Factor a perfect square on the left side:
(b + 1.5)(b + 1.5) = 4.583333333

Calculate the square root of the right side: 2.140872096

Break this problem into two subproblems by setting 
(b + 1.5) equal to 2.140872096 and -2.140872096.


Subproblem 1
b + 1.5 = 2.140872096

Simplifying
b + 1.5 = 2.140872096

Reorder the terms:
1.5 + b = 2.140872096

Solving
1.5 + b = 2.140872096

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 = 2.140872096 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + b = 2.140872096 + -1.5
b = 2.140872096 + -1.5

Combine like terms: 2.140872096 + -1.5 = 0.640872096
b = 0.640872096

Simplifying
b = 0.640872096


Subproblem 2
b + 1.5 = -2.140872096

Simplifying
b + 1.5 = -2.140872096

Reorder the terms:
1.5 + b = -2.140872096

Solving
1.5 + b = -2.140872096

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 = -2.140872096 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + b = -2.140872096 + -1.5
b = -2.140872096 + -1.5

Combine like terms: -2.140872096 + -1.5 = -3.640872096
b = -3.640872096

Simplifying
b = -3.640872096


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.640872096, -3.640872096}

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