6b^2-72b+216=0

Solution for 6b^2-72b+216=0 equation:

Simplifying
6b2 + -72b + 216 = 0

Reorder the terms:
216 + -72b + 6b2 = 0

Solving
216 + -72b + 6b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '6'.
6(36 + -12b + b2) = 0

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

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

Simplifying
6 + -1b = 0

Solving
6 + -1b = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1b = 0 + -6
-1b = 0 + -6

Combine like terms: 0 + -6 = -6
-1b = -6

Divide each side by '-1'.
b = 6

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

Simplifying
6 + -1b = 0

Solving
6 + -1b = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1b = 0 + -6
-1b = 0 + -6

Combine like terms: 0 + -6 = -6
-1b = -6

Divide each side by '-1'.
b = 6

Simplifying
b = 6
Solution
b = {6, 6}