6b^2-27b-105=

Solution for 6b^2-27b-105= equation:

Simplifying
6b2 + -27b + -105 = 0

Reorder the terms:
-105 + -27b + 6b2 = 0

Solving
-105 + -27b + 6b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-35 + -9b + 2b2) = 0

Factor a trinomial.
3((-5 + -2b)(7 + -1b)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -2b)' equal to zero and attempt to solve:

Simplifying
-5 + -2b = 0

Solving
-5 + -2b = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2b = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2b = 0 + 5
-2b = 0 + 5

Combine like terms: 0 + 5 = 5
-2b = 5

Divide each side by '-2'.
b = -2.5

Simplifying
b = -2.5
Subproblem 2
Set the factor '(7 + -1b)' equal to zero and attempt to solve:

Simplifying
7 + -1b = 0

Solving
7 + -1b = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1b = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1b = 0 + -7
-1b = 0 + -7

Combine like terms: 0 + -7 = -7
-1b = -7

Divide each side by '-1'.
b = 7

Simplifying
b = 7
Solution
b = {-2.5, 7}