-9b^2+27b-18=0

Solution for -9b^2+27b-18=0 equation:

Simplifying
-9b2 + 27b + -18 = 0

Reorder the terms:
-18 + 27b + -9b2 = 0

Solving
-18 + 27b + -9b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-2 + 3b + -1b2) = 0

Factor a trinomial.
9((-2 + b)(1 + -1b)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(-2 + b)' equal to zero and attempt to solve:

Simplifying
-2 + b = 0

Solving
-2 + b = 0

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

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

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

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

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

Simplifying
1 + -1b = 0

Solving
1 + -1b = 0

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

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

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

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

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

Simplifying
b = 1
Solution
b = {2, 1}