6b^2-54b+120=0

Solution for 6b^2-54b+120=0 equation:

Simplifying
6b2 + -54b + 120 = 0

Reorder the terms:
120 + -54b + 6b2 = 0

Solving
120 + -54b + 6b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '6'.
6(20 + -9b + b2) = 0

Factor a trinomial.
6((4 + -1b)(5 + -1b)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(4 + -1b)' equal to zero and attempt to solve:

Simplifying
4 + -1b = 0

Solving
4 + -1b = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1b = 0 + -4
-1b = 0 + -4

Combine like terms: 0 + -4 = -4
-1b = -4

Divide each side by '-1'.
b = 4

Simplifying
b = 4
Subproblem 2
Set the factor '(5 + -1b)' equal to zero and attempt to solve:

Simplifying
5 + -1b = 0

Solving
5 + -1b = 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 + -1b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1b = 0 + -5
-1b = 0 + -5

Combine like terms: 0 + -5 = -5
-1b = -5

Divide each side by '-1'.
b = 5

Simplifying
b = 5
Solution
b = {4, 5}