1.5(b+2)2b-9=90

Solution for 1.5(b+2)2b-9=90 equation:

Simplifying
1.5(b + 2) * 2b + -9 = 90

Reorder the terms:
1.5(2 + b) * 2b + -9 = 90

Reorder the terms for easier multiplication:
1.5 * 2b(2 + b) + -9 = 90

Multiply 1.5 * 2
3b(2 + b) + -9 = 90
(2 * 3b + b * 3b) + -9 = 90
(6b + 3b2) + -9 = 90

Reorder the terms:
-9 + 6b + 3b2 = 90

Solving
-9 + 6b + 3b2 = 90

Solving for variable 'b'.

Reorder the terms:
-9 + -90 + 6b + 3b2 = 90 + -90

Combine like terms: -9 + -90 = -99
-99 + 6b + 3b2 = 90 + -90

Combine like terms: 90 + -90 = 0
-99 + 6b + 3b2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-33 + 2b + b2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-33 + 2b + b2)' equal to zero and attempt to solve:

Simplifying
-33 + 2b + b2 = 0

Solving
-33 + 2b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + 2b + 33 + b2 = 0 + 33

Reorder the terms:
-33 + 33 + 2b + b2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + 2b + b2 = 0 + 33
2b + b2 = 0 + 33

Combine like terms: 0 + 33 = 33
2b + b2 = 33

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

Add '1' to each side of the equation.
2b + 1 + b2 = 33 + 1

Reorder the terms:
1 + 2b + b2 = 33 + 1

Combine like terms: 33 + 1 = 34
1 + 2b + b2 = 34

Factor a perfect square on the left side:
(b + 1)(b + 1) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(b + 1) equal to 5.830951895 and -5.830951895.

Subproblem 1
b + 1 = 5.830951895

Simplifying
b + 1 = 5.830951895

Reorder the terms:
1 + b = 5.830951895

Solving
1 + b = 5.830951895

Solving for variable 'b'.

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

Add '-1' to each side of the equation.
1 + -1 + b = 5.830951895 + -1

Combine like terms: 1 + -1 = 0
0 + b = 5.830951895 + -1
b = 5.830951895 + -1

Combine like terms: 5.830951895 + -1 = 4.830951895
b = 4.830951895

Simplifying
b = 4.830951895

Subproblem 2
b + 1 = -5.830951895

Simplifying
b + 1 = -5.830951895

Reorder the terms:
1 + b = -5.830951895

Solving
1 + b = -5.830951895

Solving for variable 'b'.

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

Add '-1' to each side of the equation.
1 + -1 + b = -5.830951895 + -1

Combine like terms: 1 + -1 = 0
0 + b = -5.830951895 + -1
b = -5.830951895 + -1

Combine like terms: -5.830951895 + -1 = -6.830951895
b = -6.830951895

Simplifying
b = -6.830951895

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {4.830951895, -6.830951895}
Solution
b = {4.830951895, -6.830951895}