b=1.5(b+2)15(2b-9)

Solution for b=1.5(b+2)15(2b-9) equation:

Simplifying
b = 1.5(b + 2) * 15(2b + -9)

Reorder the terms:
b = 1.5(2 + b) * 15(2b + -9)

Reorder the terms:
b = 1.5(2 + b) * 15(-9 + 2b)

Reorder the terms for easier multiplication:
b = 1.5 * 15(2 + b)(-9 + 2b)

Multiply 1.5 * 15
b = 22.5(2 + b)(-9 + 2b)

Multiply (2 + b) * (-9 + 2b)
b = 22.5(2(-9 + 2b) + b(-9 + 2b))
b = 22.5((-9 * 2 + 2b * 2) + b(-9 + 2b))
b = 22.5((-18 + 4b) + b(-9 + 2b))
b = 22.5(-18 + 4b + (-9 * b + 2b * b))
b = 22.5(-18 + 4b + (-9b + 2b2))

Combine like terms: 4b + -9b = -5b
b = 22.5(-18 + -5b + 2b2)
b = (-18 * 22.5 + -5b * 22.5 + 2b2 * 22.5)
b = (-405 + -112.5b + 45b2)

Solving
b = -405 + -112.5b + 45b2

Solving for variable 'b'.

Reorder the terms:
405 + b + 112.5b + -45b2 = -405 + -112.5b + 45b2 + 405 + 112.5b + -45b2

Combine like terms: b + 112.5b = 113.5b
405 + 113.5b + -45b2 = -405 + -112.5b + 45b2 + 405 + 112.5b + -45b2

Reorder the terms:
405 + 113.5b + -45b2 = -405 + 405 + -112.5b + 112.5b + 45b2 + -45b2

Combine like terms: -405 + 405 = 0
405 + 113.5b + -45b2 = 0 + -112.5b + 112.5b + 45b2 + -45b2
405 + 113.5b + -45b2 = -112.5b + 112.5b + 45b2 + -45b2

Combine like terms: -112.5b + 112.5b = 0.0
405 + 113.5b + -45b2 = 0.0 + 45b2 + -45b2
405 + 113.5b + -45b2 = 45b2 + -45b2

Combine like terms: 45b2 + -45b2 = 0
405 + 113.5b + -45b2 = 0

Begin completing the square.  Divide all terms by
-45 the coefficient of the squared term: 

Divide each side by '-45'.
-9 + -2.522222222b + b2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -2.522222222b + 9 + b2 = 0 + 9

Reorder the terms:
-9 + 9 + -2.522222222b + b2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2.522222222b + b2 = 0 + 9
-2.522222222b + b2 = 0 + 9

Combine like terms: 0 + 9 = 9
-2.522222222b + b2 = 9

The b term is -2.522222222b.  Take half its coefficient (-1.261111111).
Square it (1.590401234) and add it to both sides.

Add '1.590401234' to each side of the equation.
-2.522222222b + 1.590401234 + b2 = 9 + 1.590401234

Reorder the terms:
1.590401234 + -2.522222222b + b2 = 9 + 1.590401234

Combine like terms: 9 + 1.590401234 = 10.590401234
1.590401234 + -2.522222222b + b2 = 10.590401234

Factor a perfect square on the left side:
(b + -1.261111111)(b + -1.261111111) = 10.590401234

Calculate the square root of the right side: 3.254289667

Break this problem into two subproblems by setting 
(b + -1.261111111) equal to 3.254289667 and -3.254289667.

Subproblem 1
b + -1.261111111 = 3.254289667

Simplifying
b + -1.261111111 = 3.254289667

Reorder the terms:
-1.261111111 + b = 3.254289667

Solving
-1.261111111 + b = 3.254289667

Solving for variable 'b'.

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

Add '1.261111111' to each side of the equation.
-1.261111111 + 1.261111111 + b = 3.254289667 + 1.261111111

Combine like terms: -1.261111111 + 1.261111111 = 0.000000000
0.000000000 + b = 3.254289667 + 1.261111111
b = 3.254289667 + 1.261111111

Combine like terms: 3.254289667 + 1.261111111 = 4.515400778
b = 4.515400778

Simplifying
b = 4.515400778

Subproblem 2
b + -1.261111111 = -3.254289667

Simplifying
b + -1.261111111 = -3.254289667

Reorder the terms:
-1.261111111 + b = -3.254289667

Solving
-1.261111111 + b = -3.254289667

Solving for variable 'b'.

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

Add '1.261111111' to each side of the equation.
-1.261111111 + 1.261111111 + b = -3.254289667 + 1.261111111

Combine like terms: -1.261111111 + 1.261111111 = 0.000000000
0.000000000 + b = -3.254289667 + 1.261111111
b = -3.254289667 + 1.261111111

Combine like terms: -3.254289667 + 1.261111111 = -1.993178556
b = -1.993178556

Simplifying
b = -1.993178556

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {4.515400778, -1.993178556}