(3b-10)(b+2)=0

Solution for (3b-10)(b+2)=0 equation:

Simplifying
(3b + -10)(b + 2) = 0

Reorder the terms:
(-10 + 3b)(b + 2) = 0

Reorder the terms:
(-10 + 3b)(2 + b) = 0

Multiply (-10 + 3b) * (2 + b)
(-10(2 + b) + 3b * (2 + b)) = 0
((2 * -10 + b * -10) + 3b * (2 + b)) = 0
((-20 + -10b) + 3b * (2 + b)) = 0
(-20 + -10b + (2 * 3b + b * 3b)) = 0
(-20 + -10b + (6b + 3b2)) = 0

Combine like terms: -10b + 6b = -4b
(-20 + -4b + 3b2) = 0

Solving
-20 + -4b + 3b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-2 + -1b)(10 + -3b) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(10 + -3b)' equal to zero and attempt to solve:

Simplifying
10 + -3b = 0

Solving
10 + -3b = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3b = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3b = 0 + -10
-3b = 0 + -10

Combine like terms: 0 + -10 = -10
-3b = -10

Divide each side by '-3'.
b = 3.333333333

Simplifying
b = 3.333333333
Solution
b = {-2, 3.333333333}