(4b+3)(3b+9)=

Solution for (4b+3)(3b+9)= equation:

Simplifying
(4b + 3)(3b + 9) = 0

Reorder the terms:
(3 + 4b)(3b + 9) = 0

Reorder the terms:
(3 + 4b)(9 + 3b) = 0

Multiply (3 + 4b) * (9 + 3b)
(3(9 + 3b) + 4b * (9 + 3b)) = 0
((9 * 3 + 3b * 3) + 4b * (9 + 3b)) = 0
((27 + 9b) + 4b * (9 + 3b)) = 0
(27 + 9b + (9 * 4b + 3b * 4b)) = 0
(27 + 9b + (36b + 12b2)) = 0

Combine like terms: 9b + 36b = 45b
(27 + 45b + 12b2) = 0

Solving
27 + 45b + 12b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + 15b + 4b2) = 0

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

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

Simplifying
3 + b = 0

Solving
3 + b = 0

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

Add '-3' to each side of the equation.
3 + -3 + b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + b = 0 + -3
b = 0 + -3

Combine like terms: 0 + -3 = -3
b = -3

Simplifying
b = -3
Subproblem 2
Set the factor '(3 + 4b)' equal to zero and attempt to solve:

Simplifying
3 + 4b = 0

Solving
3 + 4b = 0

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

Add '-3' to each side of the equation.
3 + -3 + 4b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4b = 0 + -3
4b = 0 + -3

Combine like terms: 0 + -3 = -3
4b = -3

Divide each side by '4'.
b = -0.75

Simplifying
b = -0.75
Solution
b = {-3, -0.75}