9b^2-20b=-b^2+60

Solution for 9b^2-20b=-b^2+60 equation:

Simplifying
9b2 + -20b = -1b2 + 60

Reorder the terms:
-20b + 9b2 = -1b2 + 60

Reorder the terms:
-20b + 9b2 = 60 + -1b2

Solving
-20b + 9b2 = 60 + -1b2

Solving for variable 'b'.

Reorder the terms:
-60 + -20b + 9b2 + b2 = 60 + -1b2 + -60 + b2

Combine like terms: 9b2 + b2 = 10b2
-60 + -20b + 10b2 = 60 + -1b2 + -60 + b2

Reorder the terms:
-60 + -20b + 10b2 = 60 + -60 + -1b2 + b2

Combine like terms: 60 + -60 = 0
-60 + -20b + 10b2 = 0 + -1b2 + b2
-60 + -20b + 10b2 = -1b2 + b2

Combine like terms: -1b2 + b2 = 0
-60 + -20b + 10b2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-6 + -2b + b2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-6 + -2b + b2)' equal to zero and attempt to solve:

Simplifying
-6 + -2b + b2 = 0

Solving
-6 + -2b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -2b + 6 + b2 = 0 + 6

Reorder the terms:
-6 + 6 + -2b + b2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -2b + b2 = 0 + 6
-2b + b2 = 0 + 6

Combine like terms: 0 + 6 = 6
-2b + b2 = 6

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 = 6 + 1

Reorder the terms:
1 + -2b + b2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + -2b + b2 = 7

Factor a perfect square on the left side:
(b + -1)(b + -1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(b + -1) equal to 2.645751311 and -2.645751311.

Subproblem 1
b + -1 = 2.645751311

Simplifying
b + -1 = 2.645751311

Reorder the terms:
-1 + b = 2.645751311

Solving
-1 + b = 2.645751311

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 = 2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + b = 2.645751311 + 1
b = 2.645751311 + 1

Combine like terms: 2.645751311 + 1 = 3.645751311
b = 3.645751311

Simplifying
b = 3.645751311

Subproblem 2
b + -1 = -2.645751311

Simplifying
b + -1 = -2.645751311

Reorder the terms:
-1 + b = -2.645751311

Solving
-1 + b = -2.645751311

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 = -2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + b = -2.645751311 + 1
b = -2.645751311 + 1

Combine like terms: -2.645751311 + 1 = -1.645751311
b = -1.645751311

Simplifying
b = -1.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {3.645751311, -1.645751311}
Solution
b = {3.645751311, -1.645751311}