6b^2-9b-27=0

Solution for 6b^2-9b-27=0 equation:

Simplifying
6b2 + -9b + -27 = 0

Reorder the terms:
-27 + -9b + 6b2 = 0

Solving
-27 + -9b + 6b2 = 0

Solving for variable 'b'.

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

Factor a trinomial.
3((-3 + -2b)(3 + -1b)) = 0

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

Simplifying
-3 + -2b = 0

Solving
-3 + -2b = 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 + -2b = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2b = 0 + 3
-2b = 0 + 3

Combine like terms: 0 + 3 = 3
-2b = 3

Divide each side by '-2'.
b = -1.5

Simplifying
b = -1.5
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 = {-1.5, 3}