(3b+5)(b-3)=0

Solution for (3b+5)(b-3)=0 equation:

Simplifying
(3b + 5)(b + -3) = 0

Reorder the terms:
(5 + 3b)(b + -3) = 0

Reorder the terms:
(5 + 3b)(-3 + b) = 0

Multiply (5 + 3b) * (-3 + b)
(5(-3 + b) + 3b * (-3 + b)) = 0
((-3 * 5 + b * 5) + 3b * (-3 + b)) = 0
((-15 + 5b) + 3b * (-3 + b)) = 0
(-15 + 5b + (-3 * 3b + b * 3b)) = 0
(-15 + 5b + (-9b + 3b2)) = 0

Combine like terms: 5b + -9b = -4b
(-15 + -4b + 3b2) = 0

Solving
-15 + -4b + 3b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-5 + -3b)(3 + -1b) = 0

Subproblem 1
Set the factor '(-5 + -3b)' equal to zero and attempt to solve:

Simplifying
-5 + -3b = 0

Solving
-5 + -3b = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3b = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3b = 0 + 5
-3b = 0 + 5

Combine like terms: 0 + 5 = 5
-3b = 5

Divide each side by '-3'.
b = -1.666666667

Simplifying
b = -1.666666667
Subproblem 2
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
Solution
b = {-1.666666667, 3}