-b^2=9-6b

Solution for -b^2=9-6b equation:

Simplifying
-1b2 = 9 + -6b

Solving
-1b2 = 9 + -6b

Solving for variable 'b'.

Reorder the terms:
-9 + 6b + -1b2 = 9 + -6b + -9 + 6b

Reorder the terms:
-9 + 6b + -1b2 = 9 + -9 + -6b + 6b

Combine like terms: 9 + -9 = 0
-9 + 6b + -1b2 = 0 + -6b + 6b
-9 + 6b + -1b2 = -6b + 6b

Combine like terms: -6b + 6b = 0
-9 + 6b + -1b2 = 0

Factor a trinomial.
(-3 + b)(3 + -1b) = 0

Subproblem 1
Set the factor '(-3 + b)' equal to zero and attempt to solve:

Simplifying
-3 + b = 0

Solving
-3 + b = 0

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

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

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

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

Simplifying
b = 3
Subproblem 2
Set the factor '(3 + -1b)' equal to zero and attempt to solve:

Simplifying
3 + -1b = 0

Solving
3 + -1b = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1b = 0 + -3
-1b = 0 + -3

Combine like terms: 0 + -3 = -3
-1b = -3

Divide each side by '-1'.
b = 3

Simplifying
b = 3
Solution
b = {3, 3}