(4b+6)*(b+3)=

Solution for (4b+6)*(b+3)= equation:

Simplifying
(4b + 6)(b + 3) = 0

Reorder the terms:
(6 + 4b)(b + 3) = 0

Reorder the terms:
(6 + 4b)(3 + b) = 0

Multiply (6 + 4b) * (3 + b)
(6(3 + b) + 4b * (3 + b)) = 0
((3 * 6 + b * 6) + 4b * (3 + b)) = 0
((18 + 6b) + 4b * (3 + b)) = 0
(18 + 6b + (3 * 4b + b * 4b)) = 0
(18 + 6b + (12b + 4b2)) = 0

Combine like terms: 6b + 12b = 18b
(18 + 18b + 4b2) = 0

Solving
18 + 18b + 4b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 9b + 2b2) = 0

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

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

Simplifying
3 + 2b = 0

Solving
3 + 2b = 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 + 2b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2b = 0 + -3
2b = 0 + -3

Combine like terms: 0 + -3 = -3
2b = -3

Divide each side by '2'.
b = -1.5

Simplifying
b = -1.5
Solution
b = {-3, -1.5}