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

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

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

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

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

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

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

Solving
-9 + 3b + 6b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + b + 2b2) = 0

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

Ignore the factor 3.
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 '(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
Solution
b = {-1.5, 1}