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

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

Simplifying
(3b)(4b2 + -2b)(9b + 6) = 0

Remove parenthesis around (3b)
3b(4b2 + -2b)(9b + 6) = 0

Reorder the terms:
3b(-2b + 4b2)(9b + 6) = 0

Reorder the terms:
3b(-2b + 4b2)(6 + 9b) = 0

Multiply (-2b + 4b2) * (6 + 9b)
3b(-2b * (6 + 9b) + 4b2 * (6 + 9b)) = 0
3b((6 * -2b + 9b * -2b) + 4b2 * (6 + 9b)) = 0
3b((-12b + -18b2) + 4b2 * (6 + 9b)) = 0
3b(-12b + -18b2 + (6 * 4b2 + 9b * 4b2)) = 0
3b(-12b + -18b2 + (24b2 + 36b3)) = 0

Combine like terms: -18b2 + 24b2 = 6b2
3b(-12b + 6b2 + 36b3) = 0
(-12b * 3b + 6b2 * 3b + 36b3 * 3b) = 0
(-36b2 + 18b3 + 108b4) = 0

Solving
-36b2 + 18b3 + 108b4 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '18b2'.
18b2(-2 + b + 6b2) = 0

Factor a trinomial.
18b2((-2 + -3b)(1 + -2b)) = 0

Ignore the factor 18.
Subproblem 1
Set the factor 'b2' equal to zero and attempt to solve:

Simplifying
b2 = 0

Solving
b2 = 0

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

Simplifying
b2 = 0

Take the square root of each side:
b = {0}
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
Subproblem 3
Set the factor '(1 + -2b)' equal to zero and attempt to solve:

Simplifying
1 + -2b = 0

Solving
1 + -2b = 0

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

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

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

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

Divide each side by '-2'.
b = 0.5

Simplifying
b = 0.5
Solution
b = {0, -0.6666666667, 0.5}