b(b+6)=72

Solution for b(b+6)=72 equation:

Simplifying
b(b + 6) = 72

Reorder the terms:
b(6 + b) = 72
(6 * b + b * b) = 72
(6b + b2) = 72

Solving
6b + b2 = 72

Solving for variable 'b'.

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

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

Factor a trinomial.
(-12 + -1b)(6 + -1b) = 0

Subproblem 1
Set the factor '(-12 + -1b)' equal to zero and attempt to solve:

Simplifying
-12 + -1b = 0

Solving
-12 + -1b = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1b = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1b = 0 + 12
-1b = 0 + 12

Combine like terms: 0 + 12 = 12
-1b = 12

Divide each side by '-1'.
b = -12

Simplifying
b = -12
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 = {-12, 6}