3b^2=72+6b

Solution for 3b^2=72+6b equation:

Simplifying
3b2 = 72 + 6b

Solving
3b2 = 72 + 6b

Solving for variable 'b'.

Reorder the terms:
-72 + -6b + 3b2 = 72 + 6b + -72 + -6b

Reorder the terms:
-72 + -6b + 3b2 = 72 + -72 + 6b + -6b

Combine like terms: 72 + -72 = 0
-72 + -6b + 3b2 = 0 + 6b + -6b
-72 + -6b + 3b2 = 6b + -6b

Combine like terms: 6b + -6b = 0
-72 + -6b + 3b2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + -2b + b2) = 0

Factor a trinomial.
3((-4 + -1b)(6 + -1b)) = 0

Ignore the factor 3.
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 '(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 = {-4, 6}