(3b+1)(b-2)=0

Solution for (3b+1)(b-2)=0 equation:

Simplifying
(3b + 1)(b + -2) = 0

Reorder the terms:
(1 + 3b)(b + -2) = 0

Reorder the terms:
(1 + 3b)(-2 + b) = 0

Multiply (1 + 3b) * (-2 + b)
(1(-2 + b) + 3b * (-2 + b)) = 0
((-2 * 1 + b * 1) + 3b * (-2 + b)) = 0
((-2 + 1b) + 3b * (-2 + b)) = 0
(-2 + 1b + (-2 * 3b + b * 3b)) = 0
(-2 + 1b + (-6b + 3b2)) = 0

Combine like terms: 1b + -6b = -5b
(-2 + -5b + 3b2) = 0

Solving
-2 + -5b + 3b2 = 0

Solving for variable 'b'.

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

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

Simplifying
-1 + -3b = 0

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

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

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

Divide each side by '-3'.
b = -0.3333333333

Simplifying
b = -0.3333333333
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 = {-0.3333333333, 2}