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

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

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

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

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

Multiply (-2 + 3b) * (3 + b)
(-2(3 + b) + 3b * (3 + b)) = 0
((3 * -2 + b * -2) + 3b * (3 + b)) = 0
((-6 + -2b) + 3b * (3 + b)) = 0
(-6 + -2b + (3 * 3b + b * 3b)) = 0
(-6 + -2b + (9b + 3b2)) = 0

Combine like terms: -2b + 9b = 7b
(-6 + 7b + 3b2) = 0

Solving
-6 + 7b + 3b2 = 0

Solving for variable 'b'.

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

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

Simplifying
-3 + -1b = 0

Solving
-3 + -1b = 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 + -1b = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1b = 0 + 3
-1b = 0 + 3

Combine like terms: 0 + 3 = 3
-1b = 3

Divide each side by '-1'.
b = -3

Simplifying
b = -3
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 = {-3, 0.6666666667}