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

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

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

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

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

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

Combine like terms: -12b + 6b = -6b
4b(-12 + -6b + 6b2) = 0
(-12 * 4b + -6b * 4b + 6b2 * 4b) = 0
(-48b + -24b2 + 24b3) = 0

Solving
-48b + -24b2 + 24b3 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '24b'.
24b(-2 + -1b + b2) = 0

Factor a trinomial.
24b((-1 + -1b)(2 + -1b)) = 0

Ignore the factor 24.
Subproblem 1
Set the factor 'b' equal to zero and attempt to solve:

Simplifying
b = 0

Solving
b = 0

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

Simplifying
b = 0
Subproblem 2
Set the factor '(-1 + -1b)' equal to zero and attempt to solve:

Simplifying
-1 + -1b = 0

Solving
-1 + -1b = 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 + -1b = 0 + 1

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

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

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

Simplifying
b = -1
Subproblem 3
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 = {0, -1, 2}