6b^2-36b-162=0

Solution for 6b^2-36b-162=0 equation:

Simplifying
6b2 + -36b + -162 = 0

Reorder the terms:
-162 + -36b + 6b2 = 0

Solving
-162 + -36b + 6b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-27 + -6b + b2) = 0

Factor a trinomial.
6((-3 + -1b)(9 + -1b)) = 0

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(9 + -1b)' equal to zero and attempt to solve:

Simplifying
9 + -1b = 0

Solving
9 + -1b = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1b = 0 + -9

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

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

Divide each side by '-1'.
b = 9

Simplifying
b = 9
Solution
b = {-3, 9}