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

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

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

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

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

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

Combine like terms: 3b + -2b = 1b
4(-6 + 1b + b2) = 0
(-6 * 4 + 1b * 4 + b2 * 4) = 0
(-24 + 4b + 4b2) = 0

Solving
-24 + 4b + 4b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + b + b2) = 0

Factor a trinomial.
4((-3 + -1b)(2 + -1b)) = 0

Ignore the factor 4.
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 + -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 = {-3, 2}