-4(2b+3)(9b+6)=0

Solution for -4(2b+3)(9b+6)=0 equation:

Simplifying
-4(2b + 3)(9b + 6) = 0

Reorder the terms:
-4(3 + 2b)(9b + 6) = 0

Reorder the terms:
-4(3 + 2b)(6 + 9b) = 0

Multiply (3 + 2b) * (6 + 9b)
-4(3(6 + 9b) + 2b * (6 + 9b)) = 0
-4((6 * 3 + 9b * 3) + 2b * (6 + 9b)) = 0
-4((18 + 27b) + 2b * (6 + 9b)) = 0
-4(18 + 27b + (6 * 2b + 9b * 2b)) = 0
-4(18 + 27b + (12b + 18b2)) = 0

Combine like terms: 27b + 12b = 39b
-4(18 + 39b + 18b2) = 0
(18 * -4 + 39b * -4 + 18b2 * -4) = 0
(-72 + -156b + -72b2) = 0

Solving
-72 + -156b + -72b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '-12'.
-12(6 + 13b + 6b2) = 0

Factor a trinomial.
-12((3 + 2b)(2 + 3b)) = 0

Ignore the factor -12.
Subproblem 1
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
Subproblem 2
Set the factor '(2 + 3b)' equal to zero and attempt to solve:

Simplifying
2 + 3b = 0

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

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

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

Divide each side by '3'.
b = -0.6666666667

Simplifying
b = -0.6666666667
Solution
b = {-1.5, -0.6666666667}