3b(b+4)=36

Solution for 3b(b+4)=36 equation:

Simplifying
3b(b + 4) = 36

Reorder the terms:
3b(4 + b) = 36
(4 * 3b + b * 3b) = 36
(12b + 3b2) = 36

Solving
12b + 3b2 = 36

Solving for variable 'b'.

Reorder the terms:
-36 + 12b + 3b2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + 12b + 3b2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + 4b + b2) = 0

Factor a trinomial.
3((-6 + -1b)(2 + -1b)) = 0

Ignore the factor 3.
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 '(2 + -1b)' equal to zero and attempt to solve:

Simplifying
2 + -1b = 0

Solving
2 + -1b = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1b = 0 + -2
-1b = 0 + -2

Combine like terms: 0 + -2 = -2
-1b = -2

Divide each side by '-1'.
b = 2

Simplifying
b = 2
Solution
b = {-6, 2}